I live in the US, so all of our ballasts and ignitors and capacitors etc. have wire leads instead of clamp screw terminals like in Europe and other places. Anybody know why?

Wires can break off, then you are poop-outa-luck a lot of the time. Terminals are practically infinitely reusable, which is nice for enthusiasts. I have used, used, and reused many components, and the strands of the stranded wire starts to fall off. Then you have to cut it shorter and re-strip the wire. I wouldn’t have to do that if it had terminals. For a lot of my gear now, I put screw terminals blocks on them so I can connect to them without wearing out the wires.

Why does the US have to be difficult and cheap? Y’all don’t know how easy you have it.

That's a question of some local tradition, sure. Manufacturers are probably saving a little $$ on this.

Terminals DO fail too, ask me how I know Threads get stripped, push-in contacts get bent.

Push-ins certainly need a proper wire gauge and shape to work reliably.

Many film capacitors for lighting have wire leads here, too, many old Soviet ballasts from 1950-1970's were wire-leaded.

A common solution to work with wire leads is to use WAGO reusable connectors of 221 series, these are readily available in the US too and are super duper great for both prototyping and real installation work.

Ugh, those push-in contacts...  forgot about those.

I do have a few WAGOs that I mostly use for chucking stuff together for testing.

The set screw style terminals aren't that common here but I've seen the push in terminals on some electronic ballasts and LED drivers. Those generally are designed to only accept #18 solid core wire, typically used in fluorescent fixtures.

On the HID side, some ballasts used Faston quick connects instead of wires crimped to the ballast wire. The oil filled capacitors generally always used Faston quick connects and some dry capacitors are available with them as well. 

The lack of terminals was probably a cost savings measure, and also part of the general philosophy for luminaire maintenance here. When the ballasts were in production, they were not designed to be serviced and replaced as the entire "black box" when they were faulty. It made things easier back then but now it also means things like faulty capacitors aren't easy to replace.

The Wago 221 connectors are great for prototypes or for setups that you plan to swap components in frequently. I use the inline version at the lampholders on some of the fluorescent fixtures to make ballast swaps easier.