The issue is that a modified gravitational theory means getting rid of general Relativity or at least _significantly_ modifying it. As i understand, no proposed modified gravity theory has ever been able to be more accurate than GR. Every theory that's been proposed (very many for over 100 years) to resolve galaxy rotation has then failed at some other scale or situation. Most of those theories still require dark matter to explain those discrepancies. The single most accurate and explainable model currently is general relativity with some extra dark mass hiding in extremely large structures.
As well, to do away with GR means ridding ourselves of the most accurate gravitational predictions ever made. GR explains basically _everything else_. It predicts gravitational waves, black holes, the orbit of mercury and the precession of rotating bodies, as well as many other things I'm sure. And so far every big prediction has come out to be true. In physics, predictive power is everything. Most of the modified gravity theories can't even explain everything we already see let alone make accurate predictions about other things.
It just comes down to math and data. I've had this conversation with many people and while i don't want to discourage questioning or curiosity, none of these people were very versed in the actual topics of modified gravity or modern dark matter theories (not saying this about you, but I've had this conversation _a lot_). You can Google a Wikipedia article about problems with modified gravity, MOND, etc. And read about it freely if curious.
The issue i think is that it's too complicated. The science and especially the math of these theories is graduate level physics and these theories are being proposed and discounted by doctorates who've dedicated their entire lives to learning about this. It's extremely difficult for regular people with jobs and lives to have the time to truly understand the issues here, at least until someone comes along who can explain it much better than I.
I must say, I'm also not a doctorate in gr or anything, but I've been around it a while and have seen the developments unfold over time. The short answer is that modified gravity theories have more problems than gr + dark matter, at least right now.