The issue is that most vehicles take from 6 to 8 hours to complete the line. That makes it nearly impossible to indeed increase train frequency just for the rush hour.
To avoid any issue such as night frequency being operated during the morning rush, I actually make vehicles start at the same frequency during the whole 24-hour cycle. This is indeed the main gameplay flaw I've experienced so far.
The most obvious solution would be to make game minutes last longer, at least 4 seconds. I only hope this is possible without impacting other aspects such as traffic flow.
I've been thinking about this issue and it is not a problem for me. The first thing is you need to think of this as an abstraction of reality. In real life, bus routes going out to the suburbs can take 3 hours or more to make a return trip. The depot has to dispatch a rush hour bus well in advance of the time it is needed in the suburbs, so yes, your rush hour might go late into the night sometimes. In Vancouver BC, some suburban lines start running at 4:00am in rush hour mode and last trips from the city arrive in the suburbs around 3:00am.
I play the game in second speed and I find that balances nicely for me and the speed of vehicles is about right. I only slow it down when I want to watch an interchange working or to build (usually I stop the sim for this). To make this perfect, I'd suggest a settings option to use the same 48 minute cycle, but with vehicles running at the second speed - in other words, vehicles run twice as fast. It could be called "real world sim" - and should cut times for return trips in half and be closer to what you would see in the real world.
But, again, I see this as a abstraction of reality and it simulates it really well as is.