Higher rent means more people will opt to buy. That's not necessarily a bad thing in perspective. Assuming the other side effect is a decrease in costs due to a lower profit margin.
More people opting to buy means house prices go up.
There's no free lunch. The more friction, taxation, and tariffs you add to the housing market, the higher prices go for both renters and home purchasers.
If rent is higher, how will people save for a down payment?
I believe your comment is operating under the assumption that people are merely choosing to rent over buying because it's the more economically wise choice. That's not how things work in reality. Many people want to buy but cannot put up the initial costs.