Why do you lead projects if you don't enjoy doing it?

I do a bunch of stuff I don’t enjoy because it makes my life better in the long run. For example: laundry, if I don’t do it, then I have to wear dirty clothes and I am sad (and smelly).

So it goes with engineering too. Sometimes (often?) I need to do something that’s not enjoyable in the short term to realize the best long path.

I’d imagine compensation comes into play. Why do so many software engineers go into management?

Compensation not only in terms of getting more, but also in terms of keeping it from dropping off. Good luck fending off ageism if you don't shift into more managerial roles.

I enjoy some parts of it, but writing code is what makes me happiest - and I don't get to do as much of that on my own time as I'd prefer.

And as others pointed out, because if I refuse to, I'd likely eventually be let go.

The insane cost of housing, mostly.