Not quite. Miners will do whatever gives more benefit to themselves. Is the 21 million BTC cap good for them?
Yes, it is. Without it, their BTC would become worthless.
Would it?
Let's suppose, just for argument, that the majority of the miners decided to raise the cap to 210 million BTC, and lower the difficulty so that mining became 10 times more productive in BTC terms. What would happen?
Note that the total supply of bitcoins would not
immediately increase, there would still be only 12 million BTC "in existence". The flow of mined bitcoins would increase by some factor, but it would still be years before the remaining 9 million "old" BTC are mined and the "new" bitcoins start to be broken into. The market value of bitcoin may drop somewhat, because of the loss of the "scarcity" aura (which was lost anyway when the altcoins sprung up); but it may also go up, because the future viability of mining would look less uncertain. The utility of bitcoin as a medium of payment would not be affected (except perhaps momentarily by the change in market price); on the contrary, bitcoins would eventually be more evenly distributed, and a larger slice of the pie would go to those who are actually making bitcoin work. And the increased "inflation" rate due to higher mining output would discourage hoarding.
Miners who chose to remain faithful to the "classical" protocol, with its cap and difficulty, would be making 1/10 of what their colleagues are doing; and will lose all their output if they fork and the other chain prevails. Why would they do it?
You seem to be assuming that all miners are hoarders. But they already must sell a large fraction of the BTC they mine in order to pay their energy bills and other expenses. Many miners probably sell
all their production, in order to have the profit in cash now rather than hope for the hypothetical future when one bitcoin may be worth a zillion dollars. These miners do not care if the present BTC owners will own only 5% of all the money in that fantastic future, instead of 50% of it.
Note, I am not saying that this
will happen, that its is
likely to happen, or even that it would work in exactly those terms. I am only pointing out that miners' greed (or simply their need to make ends meet) may well destroy bitcoin's supposed scarcity, rather than protect it.