Other countries have seatbelts on school buses, so it's not exactly some cut and dry question.
It's not even the case in all US states.

The NTSB recommends that we start enforcing seat belts on school buses.
https://www.ntsb.gov/Advocacy/safety-topics/Pages/schoolbuses.aspx

They agree with what you said, but disagree that the risk of being trapped outweighs the risk of being fired face first into a seat back.

An interesting stat about school buses is that over the last 20 years or so, there has been a roughly equal number of bus driver deaths and passenger deaths. Since a school bus typically carries a much larger number of passengers (as many as 70 or more) than drivers (1), this means that the risk of death for the driver is far higher than that for the passengers (although exactly how much riskier it is is difficult to determine from the published data).

Another interesting safety feature of school buses is that the bus bodies are clipped to the chassis rails rather than being bolted or welded to them and thus are held in place solely by friction. This is so that the bus body can slide forward a couple of feet along the rails in the event of a head-on collision, which greatly reduces the deceleration forces experienced by the passengers (this crash test video shows the phenomenon clearly). This does not help the driver much either as they're sliding forward into the engine compartment or into the oncoming vehicle in the case of flat-front buses.

It’s pretty unlikely that the bus would roll

Yeah, buses really aren't going to roll unless they get hit hard on the side by an equally-large vehicle traveling at a high speed - or unless they run afoul of some mythbusters.

The fire stuff makes some degree of sense but the "padded seat" thing doesn't. 1) they aren't very padded in the back, and 2) by that logic people wouldn't need to wear seatbelts if they sat in a back seat in any car.

"padded seat back in front"

I haven't had to take a school bus in 20 years but from what I remember there isn't much padding over the frame that goes around the back so I wouldn't want to get that in my face in a crash!

I just want to point out that decapitation, in a medical sense, doesn't necessarily mean the head is removed from the body. You can be internally decapitated.

School bus drivers have more oversight than police huh?

School bus drivers are going under significantly less training and requirements in my affluent DC suburb, since Covid at least.

They don’t get paid shit and they’re privatizing the school busses :(

Iirc, Mythbuster tried to roll a bus and couldn't.

Nope, it's literally a cost benefit analysis.

https://www.nhtsa.gov/document/seat-belts-large-school-buses

NTSB recommends seatbelts, NHTSA says they would save lives, but the cost or complexity might reduce usage, and school buses are safer than being dropped off at school, so the cost isn't justified.

Train has entered the chat

It’s because in the event of an emergency it is harder to get them out

Because an adult should know how to unbuckle themselves in a rollover accident.

And the driver is at a different impact point

The back of the seat if front of the students is higher and softer than the steering wheel in front of the driver.
As unfortunate as it sounds, in most accidents kids can't bounce around much and mostly hit something soft enough to keep injuries minor or at least nonfatal.

For a long time the numbers worked out that that was enough for most bus accidents to protect students, and that seatbelt costs would be better spent increasing safety at pickup and dropoff locations and increasing bus ridership numbers, since even without seatbelts a school bus is radically safer than being driven to school or walking in most places.

More recently, the numbers have started to say we should invest in seatbelts and making pedestrian routes to schools safer, since those would now make a more significant impact.