This isn't my experience, but I understand some countries have overloaded public transit systems. When I've been in those countries, it's been simple enough to just let an overloaded train pass and grab the next one.

Ok but you let that train pass you might lose the connection to the bus at the other end. Or the next train or bus might not be for half an hour. Now you're late to wherever you were going.

Right, so, again, it sounds like your public transit is underfunded or something. Where I live I can depend on there being another train within 8 minutes no matter where I'm going, or a bus, or I can just hop on a ubike and I can be confident there'll be a space and station within a couple hundred meters.

I sympathize with people that aren't so lucky, but, if Taipei can figure it out, there's really no excuse elsewhere. Good public transit really is the only viable way to move people. The private car is, objectively, the worst.

During the rush hour, the next train is going to be just as packed. And if you wait long enough for things to quiet down, you're not going to be at work on time.

This doesn't happen to me where I live. It's time to increase your city's transportation budget!