Pretty much any decent mass transit system in the world is packed at rush hour. The whole advantage over private vehicles comes from the fact that people take up less space.

I agree it's a fairly common issue but I feel like it's not an impossible issue to solve. A person and a bike is still massively smaller than a person in an SUV. The system is basically designed with just enough capacity to barely work. But I feel like if we really wanted PT to be the obvious best choice it should be provisioned a bit over the least possible capacity.