I know quite well how a phone update is created, so let me explain:
Step 1. Google creates OS. The OS does NOT include: drivers (radio driver, S Pen driver, etc. It may include some basic drivers, but definitely not all drivers since each phone is different). It does NOT include: manufacturer customization (TouchWiz, Sense, etc.) or carrier -specific apps (visual voicemail, etc.).
Step 2. Manufacturer adds drivers and customization. The drivers will be slightly different for each variants of the same model. For example, T-Mobile Note 4 and Verizon Note 4 need different radio driver because one is GSM, and the other is CDMA. T-Mobile and AT&T have very similar radio technologies (GSM/WCDMA/LTE) and the drivers should be very very similar, if not exactly the same. I suspect they actually have the same radio chips and same drivers, but may need some tweak to work better in each network. Also, the radio drivers are probably provided by Qualcomm. Other drivers (GPS, S Pen) should be exactly the same.
Step 3. Carrier gives their APKs to manufacturer so they can be integrated into the ROM. It's possible that the carrier has in-house team to develop the bloatware, or they may out source the development. Either way, the carrier lacks expertise/resources/access to do the integration directly. Note that some apps, like Wi-Fi Calling, may need deeper integration than simply installing the APK.
Samsung probably has one team working on both AT&T and T-Mobile Note 4 updates, because they are so similar that having one team is the most efficient way (both time and money). In fact, if carriers don't require branding difference (like the logo and boot animation) and built-in apps, Samsung could just release one phone for both AT&T and T-Mobile. Of course, there may be different team members or even sub-teams working on the differences (like built-in apps), but the vast majority of the update is the same, and it's unlikely that Samsung started working on the T-Mobile update much later than the AT&T update.
So, what delays the T-Mobile update? OS is the same, drivers are (almost) the same, manufacturer customization is the same, Samsung update team is probably the same, the only difference is the T-Mobile apps. Possible reasons:
1. T-Mobile gave APKs to Samsung pretty late
2. T-Mobile's APKs are buggy
3. T-Mobile's APKs are not fully compatible with Lollipop + 2K display
4. T-Mobile's internal testing of Note 4 is delayed for some reason, but they still leave the update state in "Manufacturer Development" so they won't take the blame.
And other T-Mobile related reasons...
Dear T-Mobile, your comment?