They had a rocket they needed to test (Falcon Heavy) and that requires a test payload. Usually test payloads are boring mass analogs. Instead they decided to use something different and get a bunch of marketing out of it. Everything had to be approved by the appropriate government agencies well ahead of time. So where does the "spite" come from?

I can't find the reference now, so perhaps I hallucinated it. But as I recall, the car was intended to go to another investor, and the early-Tesla investor/CEO shenanigans put it into limbo, and so Musk launched it.

Interesting story if true. Why would Elons personal roadster have been promised to an investor?

The alternative was literally a lump of concrete.

That was the Falcon Heavy test launch and he wasn’t able to even give away the flight for free to anyone when he offered.

It only happened once, which was an obvious marketing stunt that presumably served its purpose. There's not much benefit to doing it over and over again.

If he was really doing it "for the lulz" then there would be many more such launches. Cars, a painting of some artist that offended him, etc. We haven't seen that though.