Sizing transistors for linear operation will become very expensive. Because with higher voltage than about 3..4V across the FET, the allowed current droops very rapidly, usually ~1/Vds^2. The problem is, the FETs do suffer from thermal instability over their silicon area in a similar manner as bipolars do. Claims like "FETS do not suffer from second breakdown" is not true anymore, once the FETs reached the low Ron and so the high current capabilities. It is displayed in the SOA chart...
With the pulsing it is worse than a single pulse, but still tolerable. The point is that way it allows to use transistor way smaller than would be needed to drive the full cold lamp current (about 14x the nominal), yet stay within the safe operating area of the transistors. Mainly when integrated into some more complex IC (one chip driving a bunch of bulbs and so on, where the silicon area (needed fot brutt force power) is way more expensive than discrete transistors, but the density of small transistors allow to integrate way more complex control into fraction of the power element on the chip. Or whenlarge currents are involved, so a microcontroller alowing the more complex scheme is cheaper than the brute force power transistor sizing.
Such warmup burst uses to be some dozen of pulses, so not that much stress from the battery ripple. But having similar thing present all the time could wear the input connections (reverse battery protections and the input capacitors in many of the electronic modules). Plus it may affect many sensors, temporary burst of inaccurate data from the sensors could be ignored (the car electronics count on such starting bursts happening from time to time), but for longer time would cause problems (may trigger fault codes, so they should not las for so long).
The alternator has no problem at all, as it won't respond that quickly anyway, such surges are handled solely by the battery. The alternator only takes over the average current, just maintaining the battery charge level balance...
Using high frequency DCDC means way more complicated and demanding power circuit, you need to put all the smoothing within the control box. Way too much hassle for something as slow as an incandescent.