It's actually thought that Kessler syndrome is kind of already happening right now, which is why there's a lot of push right now to try to de-orbit the very large pieces of debris, so they can't act to form further debris.
I’m sure I’m missing something but it just seems like a no brainer to make the deorbit process speed up with something relatively failsafe, as opposed to hopefully/maybe saving a bit of fuel to push it that way eventually
2. Engines and fuel are heavy. Including one on the smallest satellites may take up the entire mass availability that would go to the instruments, leaving the satellite with nothing to do. There are people working on this, one idea is including a small air canister and a balloon. At end of mission the balloon can be inflated which greatly increases the drag of the satellite causing it to de-orbit relatively soon.
3. As a side note, you don't want to fire "out to the expanse" as that won't de-orbit your satellite. It'll just "twist" the orbit, lowering the perigee and raising the apogee. Primarily it'd just waste fuel. To de-orbit you want to slow down, so you need aim "backwards" along your orbit's path.
4. With a big mass you need an equally large amount of fuel as what determines your ability to de-orbit is the satellite mass, your engine's propulsion efficiency, and the amount of fuel you have.
5. The problem isn't existing satellites. The problem is very old defunct satellites and rocket bodies and existing small debris. Many rockets used to (and still do to some extent) leave large pieces of themselves in orbit.