T-Mobile has been managing how many people they sign up in an area. Sometimes T-Mobile's home internet is available in your area, but then they get a certain number of signups and it becomes unavailable in your area until they're able to increase capacity or customers cancel. It's possible that it was available in their area and others signed up for it.
AT&T is only offering service in very limited areas and it seems like they're mostly trying to replace their DSL connections that they don't want to upgrade to fiber.
Verizon's service is currently pretty small scale, but they're looking to grow it. Again, it will be limited areas because no one wants to overwhelm the network.
Even if you have good phone service, there's a big difference between someone using 10GB on mobile and someone using 500GB as a home user. Signing up 10 home users could be like adding 500 new phone users in a small area. That can be a lot of traffic and they don't want to start seeing their mobile users cancel service because home users are clogging up the network. So they want to roll it out a bit slowly, especially as they increase capacity over the next few years with midband 5G.