London underground looks awesome, but I can't imagine it having even the vaguest utility in terms of knowing when to leave the house.

Because it's a metro service (some peak periods have 36 tph throughput), in most cases the answer will be that you should leave when you want to travel and then a train turns up and you board the train, so you don't need this information. But, the services may be disrupted or unavailable and that might mean you make different choices e.g. Victoria's main line was shut due to a One Under when I was there at Xmas, so I took a bus to a station that wasn't shut and continued the rest of my journey.