People would remain to the fork they accept which isn't incentivizing miners.
Not necessarily. People choose the fork that they deem to be better for the community in general. Given the various stakeholders, either you come to a compromise or you choose the best for yourself.
So, if the people migrated to the fork that wouldn't change Bitcoin and most of the miners to the one that benefits them the most, the security of the unchanged fork would decrease, but the money would remain. Thus, it'd be more profitable for the miners to mine what people follow and not what is benefiting them in the protocol level.
Miners don't want the network to split, simple as that. If there comes a day that miners or the community are willing to destroy Bitcoin, by having a hard fork that separate the key stakeholders (or economic agents), then Bitcoin is doomed. It isn't about what chain is more profitable to mine on or which has more security, it is about making the rational decisions for themselves, by looking at the bigger picture. If you tarnish the reputation of Bitcoin and/or otherwise destroy the confidence of the general public and potential investors, then you're just digging a hole for yourself.