And what prevents greedy people from forming Bitcoin to remove (or increase) the maximum coin count and getting enough other geeedy miners to go along with it to be the majority fork?
The nodes define what a bitcoin is. So long as they agree that bitcoin should follow the original exponentially decreasing reward schedule, then that is what will happen.
There are some problems, for instance, if almost all miners decided to switch to another fork, then the original chain would simply die because of the difficulty. But miners have electricity bills to pay and are strongly incentivised to mine the most profitable chain. It is not a matter of convincing the miners, but of convincing the world that your uncapped fork is more valuable.
I just want to point out that difficulty decreases when there's less mining. Difficulty would not be the problem. Bitcoin would just be more vulnerable to a 51% attack with less hash power.
This is even worse because it would likely be corralated with a loss of market value for Bitcoin, which lessens the incentive to mine. Combined with the ease at which miners can switch to another coin (or, at least, another bitcoin fork), and it is easy to imagine a death spiral where Bitcoin simply fails to lower its difficulty because it does not have enough hashrate to do so.