LEDs exist that are approximately the color of LPS lamps. I will refer to these as "amber" as they are often called. Two types of these LEDs exist:

Phosphored:
 - Just a blue LED with phosphor on top that converts it to amber light.

Monochromatic:
 - The actual diode emits amber light (no phosphor), this light is monochromatic, similar to LPS.

As a side note, if you want to mimic the appearance of HPS, phosphored LEDs would be best because they have a CRI more similar to HPS. If you want to mimic LPS light, obviously you would want to use the monochromatic LEDs.

But, if you just need an amber indicator (power indicator, turn signal, etc.) I would think the monochromatic LEDs are the cheapest, but this is not reflected in the majority if products I see. Specifically, on side-view car mirrors, an amber LED indicator is often employed as a warning that another car is in the lane next to you. Almost every single one I have seen has shown a strong blue presence (using my glasses as a cruddy spectroscope), indicating that phosphored LEDs are being used.

Why would they do this? What advantage is gained?

There are two reasons:

First with any light source or even any material dealing with light and vision used around cars you want to avoid as much distortion of colors things have as possible, as colors are very important factor in distinguishing various signs (speaking about the majority of the world, not just the North America). So even in case of an "amber" signal light, you want the colors of illuminated objects to remain readable. That means even when that light may need to appear amber, it must still contain some power in the whole spectrum. A filtered incandescent or a bule LED with phosphor allows that, inherently monochromatic LPS or direct LED does not.

Second reason is, the "blue+phosphor" is just way more efficient than direct amber semiconductor LED, so you suffice with less power to drive it, so less heat dissipation to deal with, so overal cheaper way.

@Medved
Thanks, that definitely explains it.\

I had no idea that phosphored LEDs were more efficient, I guess that has something to do with the efficiency of the exact type of LED used.

The phosphor conversion losses are just less than how much the "classic LED technology" loses when moving away from the IR optimum (for GaAs).
Plus in the last 20 years or so, there have been way more money thrown into the "blue chip + phosphor" technologies than to the "tradditional LEDs". So naturally one should expect way more progress in that direction...

One obscure reason to prefer phosphor converted LEDs in red and in yellow is forward voltage. As phosphor LEDs use blue light source, they share approximately the same forward voltage with blue and green LEDs which enables to use them on parallel strings without individual ballast resistors, like in christmas lights.

Also, at least for my eyes, phosphor yellow and greens have softer colors, not as toxic looking as bare yellow and blue-green chips, more pleasing in decorative lights.

 

The phosphor conversion losses are just less than how much the "classic LED technology" loses when moving away from the IR optimum (for GaAs).
Plus in the last 20 years or so, there have been way more money thrown into the "blue chip + phosphor" technologies than to the "tradditional LEDs". So naturally one should expect way more progress in that direction...

Actually, there is a silent revolution in red, orange and yellow LED efficiency going on currently. There is a demand for efficient reds for agricultural lights, without phosphor conversion, and Osram offers some impressive chips. Also, for a little premium, direct high brightness oranges and yellows are available now, already quite bright at just one milliamp.

The main reason is cost - the highest efficacy phosphor-converted amber LEDs are about 3x cheaper than pure amber - and on top of that there is the efficacy advantage of PC types so the difference in terms of cost per lumen is even greater.

There is also a very significant life improvement for the PC types, whereas pure amber quickly diminishes.

For automotive applications, pure amber LEDs are often forbidden due to their peak wavelength not matching the allowed chromaticity across the whole ambient temperature range.  The dominant wavelength of those chips is very sensitive to temperature, and in some outdoor conditions when used as turn signal indicators their colour is too close to the red to be permitted.

As such the direct amber LEDs are rapidly dying out.  They remain mainly only for tiny indicator LEDs where the customer has little interest in performance, and it can be cheaper to make a very low output device than blue+phosphor.  Or in spectrally sensitive applications that absolutely require their narrow wavelength vs PC types.  Recently I had such an application to develop LED filament lamps with direct amber chips, to replace SOX lamps in the French champagne industry.  The wavelength of the PC amber types is too broad and negatively impacts the flavour.  In such an application the cost is much less important, and pure amber LEDs can be justified.  The same is true for lighting the darkrooms of some certain photographic film production plants

At work, we are using literally tons of direct yellow LEDs for indicator application (small 0603/0805/1206 SMDs). No sign of any converted yellow LED components slipping in yet. Also, performance degradation was never noticed. Direct yellows have a distinct advantage here of having forward voltage low enough to be reliably driven from 3.3V logic.

As such the direct amber LEDs are rapidly dying out.  They remain mainly only for tiny indicator LEDs where the customer has little interest in performance, and it can be cheaper to make a very low output device than blue+phosphor.  Or in spectrally sensitive applications that absolutely require their narrow wavelength vs PC types.  Recently I had such an application to develop LED filament lamps with direct amber chips, to replace SOX lamps in the French champagne industry.  The wavelength of the PC amber types is too broad and negatively impacts the flavour.  In such an application the cost is much less important, and pure amber LEDs can be justified.  The same is true for lighting the darkrooms of some certain photographic film production plants

Spectacular story. I wonder how big the taste difference is. I'm no stranger to being able to focus on the most minute changes in sound quality, but i've never thought just the ambient light in champagne production having an influence on the taste in the relatively short time it would be exposed to it in the bottling plant.

If you have any more of these, don't hesitate to write them down somewhere and draw our attention to it!

Funnily enough, years ago i tried making my own amber darkroom lighting (i do darkroom prints). My paper got fogged much faster with the amber leds i bought, than with red ones. I wonder if i have some left over from that project to test and see if they're phosphor converted LEDs. That would explain a whole lot.
I'm gonna try out my Osram Duka 10 LPS darkroom lamp one of these days, it may also just be the paper that just happens to be somewhat sensitive to yellow or the fact that a handful of fairly bright amber LEDs are much brighter than the old school 15w deep red incandescent lamps that were once the standard.
I do black and white, while amber darkroom lighting is mostly used for color photographic paper.

I've two orange LED nightlights with direct orange LEDs. They did lots of hours and dimmed slightly, but still usable.
I think that phosphored orange LED would have worse lumen maintenance than direct orange LED, as the phosphor degrades much faster than the die itself.

Even the direct amber LED chips are not that narrow band, they are reaching quite into yellow, quite close to green, vs the LPS which is really monochromatic. The shorter wavelength tail could also cause some hazing.
The phosphor coated will have really visible high energetic (means visible on the spectrum) blue peak, I would guess this would make the photo paper really black, not just slightlu hazy...

The ones i used were more sodium yellow than orange-amber. But it's been a while. I'm sure they're floating around in one of the boxes with parts, or perhaps there's one left in my LED drawer.

@Medved
I didn't know that, I thought they were just as monochromatic as LPS or maybe more so, but I guess that is why they don't use them as monochromatic light sources.

@Laurens
I just call them amber because they kind of look like "amber" turn signals, they appear very much like the shade of yellow emitted from an LPS lamp.