You buy a second server. Now, your server still is overloaded between 08:00 and 9:00 but fewer people use it between 07:00 and 08:00 and 09:00 and 10:00.
There are plenty of people avoiding the main traffic times for whom the annoyance of congestion is just a tiny bit larger than the annoyance of leaving home an hour earlier. Take away a bit of congestion and they move their schedule.
Your analogy is broken because building more servers doesn't "get more users". You have to service a fixed number of users in the most efficient manner possible. Providing a car lane for each of them is not efficient.
So I open another stall next to it but the lines don't seem to get much shorter even though I'm making twice as much coffee.
Notice that nowhere in there was a requirement that said infrastructure pays for itself. More often than not, and especially in small towns, it doesn't.
But don't believe me, take it from a civil engineer and urban planner who has done a lot of real research into this phenomenon: https://www.youtube.com/watch?v=tn7aJ_Ti-co
You're assuming that having more roads makes it more efficient, but that's not necessarily true. If having less urban roads convinces more people to use mass transit, for example, it might be more efficient.
So you buy another server. Now you have 2000 users, but once again it is starting to run slowly.
You decide to stop there. Clearly, more servers wont help. You'd just get more and more users.