Persistence hunting likely wasn't a major driver of those evolutionary changes.

The hypothesis is really only supported by the fact that we have adaptations that make it theoretically possible, but the times and places those adaptations came about doesn't really match up with the times and places it would have been effective (i.e. woodland where the ground would be too hard for effective tracking [0]).

There are some other things that point away from it, too; it's worth doing some googling.

It's certainly possible that persistence hunting happened to some degree, and it's a fun idea so it really caught on in popular consciousness, but the actual evidence is limited.

[0] https://www.sciencedirect.com/science/article/abs/pii/S00472...