Sorry to disappoint you, but TMobile IS working on the 5.1 update for the Note 4. That being said, it doesn't mean it'll be out quickly. Yes, updates have improved with both manufacturers and carriers lately, but it's still not perfect. The first update comes from Google, and then manufacturers have to adapt that to their custom OS's for each of their phone models. Once that's done, carriers further tinker with this because, well, they add their own software and modifications.
Why does it take more time for manufacturers, and furthermore, for carriers to come out with updates and why some 'old' models might be left forgotten? Man power. Google has a team that handles the updates to the OS, but that's a general OS. The reference OS. Manufacturers need to assign a team to apply the update and modify it to fit their custom OSs and specific hardware configurations for their different models. For instance, for Samsung alone, this means at least working on updates for the Note 4, Note 5, Note Edge, Galaxy S6, Galaxy S6 Edge, Galaxy S6 Edge+ as their 'first priority', not to mention the Alpha line, their mid-rangers, tablets, etc. and each and every variant of the same model family (AT&T Note 5, T-Mobile Note 5, Sprint Note 5, International Note 5, etc.). Once it trickles down to the carriers, they also need a team to work on adapting said updates from the manufacturer to their own further additions and modifications. And for carriers this means a myriad of phones from all manufacturers.
In the end, they do have to prioritize which phones they want to focus in first, and usually, those are the newest and greatest top-of-the-line phones.