Convincing should be pretty easy if the rule change goes against the interest of the majority of the bitcoin community. And if it doesn't we don't have a problem in the first place.
Why should the miners take such a huge gamble. What kind of rule change would justify taking such a risk?
For definiteness, consider postponing the next halving by 2 years, but then reducing the halving interval to 2 years instead of 4, so that the total issuance woudl still be ~21 M BTC.
That change would means something like 150 million USD of extra revenue over 2 years to a majority mining cartel. (Too lazt to check the number now, but it is that order of magnitude.) That obviously could make the difference beween getting rich or going bankrupt,
So, the motivation for the miners would be very strong. All other players would be against that change in principle, because the would see little gain (or some loss) for them at various time scales, and "the protocol is sacred". But, if the change were to happen, they would not be directly harmed, and could live with it.
Would the cartel be able to impose that change on the rest of the community? I believe that it would. The "self-interest" argument works better the other way: why would the "economic majority" crash the price and lose all their investment, by trying to fight the cartel? In order to protect their investment, most holders and companies would pretend to approve the change, and would tell everybody that it was "good for bitcoin"...