Is it normal to go into a PhD not having at least a vague thesis topic?

I had the opposite issue -- I had an idea that had support in my research area, but my advisor did not have funding to pursue.

(I wanted to expand the end of term project I did in a class whose professor hired me on as an RA and wrote one of my rec letters)

I eventually left, because if I am going to be told what to do, I can do that for more money and less stress outside academia.

(Forgive the vagueness, but my former area is a small world and I don't want to dox myself)