Similarly, switch fouling time is another constraint: you don't want to move a switch while a train is allowed to path over it, in case the switch fails to switch. From what I've heard of existing urban systems, this leads to a minimum headway of ~90s, although I don't know how much of that is signal-induced padding.
The next thing to point out is that these are theoretical maximum density; the practical maximum operational usage is generally far less. Most subway systems have the physical capability of operating ~45TPH on a subway line, yet you'll notice that extremely few do. Moscow Metro has managed 40TPH on an unbranched line; branched lines struggle to get to 30TPH, and heavily reverse-branched systems like the DC Metro or NYC Subway struggle to make even 20TPH. Introduce branches into the mix, and you need trains to make it onto the mainline in slots, and there's going to be variance in arrival time because the system is used by humans; reverse branches makes the problem worse because these slots need to line up well on multiple lines at the same time.
> Trains would be able to hitch and unhitch whilst moving 100 mph, allowing different loads to be sent different directions and different sets of passengers to stop at different stations.
No. There's a reason railroads have banned the practice of unhitching at speed (it's incredibly dangerous), and hitching is even worse. And if you're talking about EMU passenger train sets, most of them are designed to not be hitched or unhitched particularly frequently--these aren't your standard automatic coupler system (which doesn't couple brake lines or electrical lines or other things automatically anyways, FWIW).