Today's gentrification is caused by wealthier people moving into neighborhoods, and making them less affordable. BUT this affordability reduction is relative to the price we were at before.
The price we were at before is already extremely unaffordable due to insane building restrictions and a NIMBY attitude baked into regulation.
If the city allowed the building of high-rises everywhere, would gentrification stop? No. Certain neighborhoods would get gentrified, and become relatively higher priced. Overall, however, city affordability would skyrocket.