I think it is quite simple. Just apply net neutrality rules to this like any other internet connection.
If they can afford to support whitelisted messengers at a very limited data rate of 1k/s then they can afford to simply give people 1k/s of neutral internet access to use to communicate whatever data they feel is high value enough to fit over those constraints using any protocol they wish.
We already have internet access over HAM radio via net44. Highly bandwidth restrictive because of physics, but you can get a permanent IP assigned to your callsign and use whatever software you want with your tiny bandwidth pipe even in the middle of the ocean.
I don't think the speed of text messaging allows for many other meaningful data types. Someone encoding video into the GSM-7 format used by SMS will still consume more data than the typical person typing and sending text messages (which is what, 140 bytes each way per minute on average?).
There is also the difference between free and paid. Sure, if you're paying, you should be able to do whatever you want at the advertised speed and data limits. But for a free feature, I think it's alright to limit to SMS and other texting apps (already done on inflight wifi and it works just fine).
Why not just limit to SMS? Because travelers' home carriers might levy roaming charges on SMS, and WhatsApp / Telegram / iMessage is already de facto in most of the world.
This is exactly why net neutrality rules were a bad idea, because of insane proposals like this that would kill legitimate innovation. If you are lost in the woods without a cell signal, you don't want someone downloading a podcast episode at 1k/s sucking up all the bandwidth.
Maybe they are downloading a low res video demonstrating an emergency field medicine procedure to save a life far from hospitals. Maybe they are a journalist or a whistleblower uploading a picture that may change the outcome of a war.
A central party trying to decide what data is most important is going to be wrong when it counts most.
If a single user is monopolizing all bandwidth and a new user joins, throttle the existing user in half to make room.
There might also need to be a way to signal a need for emergency bandwidth, 911 style, that can give you priority access for a short time window, with the option for a carrier to cut off your device IMEI entirely if it is used too frequently.
In practice though they want to offer bursty throughput. For example, if you want to allow sending photos in messages, but not videos, you don't want to send a photo at 1k/s. It's not a trivial problem.
If they can afford to support whitelisted messengers at a very limited data rate of 1k/s then they can afford to simply give people 1k/s of neutral internet access to use to communicate whatever data they feel is high value enough to fit over those constraints using any protocol they wish.
We already have internet access over HAM radio via net44. Highly bandwidth restrictive because of physics, but you can get a permanent IP assigned to your callsign and use whatever software you want with your tiny bandwidth pipe even in the middle of the ocean.