Just what would you like to do with Newton, which is still damn useful when not dealing with extreme speeds or gravity? Throw it all away? And replace it with what?
You're still not explaining well what the problem is. Science throws stuff away all the time. In fact right now scientists would LOVE to throw out Relativity AND Quantum Mechanics and replace it with something thats compatible, they just haven't found it yet. But they keep looking, to the tune of building massive colliders hoping to find SOME results that don't match. Thats where you are dead wrong. Scientists WANT to find new things, find data that doesn't fit. Because that means they found something NEW, and that, is why they are scientists in the first place.
You're still doing it. You're holding the current system up and expecting me to answer in terms of it. I'm saying no, I'm saying that's the flawed approach. By rights there should be way more than one mainstream, all developed independently, held to the same standard of needing to provide accurate explanations, and allowed to develop to an equivalent standard rather than being rejected simply because a younger model would lack depth. Start from scratch using knowledge, possibilities and conclusions that we have come to using greater technology. Don't throw anything away, but be prepared to build other possibilities. There should be multiple mainstreams, all functional by tweaking and observation, but all with different basic principles. That at least would allow for error. And when there's a new discovery that would alter any starting point, make a new model based on that. The one held as true would be the one that wins an honest comparison to see which requires the most special pleading, but the door would always be open for another to take the reins. Science does
technically do this, but on such a piddlingly small scale. It's verboten to question anything 'established,' and I'm saying that's wrong, open the doors to consider far more, put whole models to the test as opposed to tiny side elements on the frontier, that would at least be intellectually honest.
Would it be slower? Yes, absolutely, but speed isn't what matters. Accuracy and truth is.
Science isn't looking to throw out relativity or QT, it's looking to give it the Newton treatment, "Well it works so we'll say it holds in this situation, but not this one..." refining and adding, not replacing.
That's the problem. The scientific community just isn't equipped to deal with a long-held flaw. Even the examples you bring up of things that might get tweaked are more recent, comparatively speaking, developments. If a flaw gets brought up with something like, say, gravity, they're just going to assume the theory was right and invent, say, dark matter or some equivalent to make it work, rather than go back and rethink the starting point. And why? Because almost everything has been built on that starting point. The scientific community has become a top-heavy unwieldy mess, and its refusal to rethink the basics means all that's keeping it going is a hope, prayer and a whole heap of denial.
Ultimately though, the heliocentric model won out. It took a long time but ultimately science will replace models if new ones come along which fit observations. I don't think in this day and age it would take as long as it did in that case because of better communication and collaboration.
Ultimately, if a model has been demonstrably working for centuries it's going to take some pretty compelling evidence to replace it.
That's a very flawed comparison. Flaws with the geocentric model, under RET, had been identified for ages, there was no good explanation for epicycles, it was merely 'we need this to happen, so it does.' The problem wasn't equipment, the problem was a theocracy. It isn't a sound basis for comparison because nowadays, at least internally, the scientific community lacks those specific pressures. The problem is that a 'new model that fits observations' is never going to happen because of the sheer amount of knowledge we now have compared to then, a new model that fits observations in even half the detail RET does is going to take decades to develop. That's no measure of truth, that just means math takes a while to develop, models time to put together, and the mainstream has been nipped and tucked and tweaked to force it in line with those experiments. Creating another that the mainstream would be willing to even consider is not going to happen regardless of what model is true.
RET hasn't demonstrably been working for centuries. It's run into problem after problem, it's just that they solved those problems internally as opposed to seeing what alternatives could do, and the longer that goes on, the harder it's going to be to make them look at anything outside their comfort zone. If a flaw in it gets pointed out tomorrow, we're a week away from it being heralded as evidence of some new facet of RET. That's how the community works now. There's no room to question the principles.
And that's where the comparison to Galileo comes in. Heliocentrism required fighting against the religiously enforced geocentric worldview to be accepted, but at least there was an enemy to disprove. Now the scientific community has taken on the same religious mindset when it comes to venerating those that came before, it is its own theocracy, and an enemy within cannot be fought so easily.
That's where we enter into 'tear it all down' territory. The modern scientific community has become so poisoned I honestly don't know how it can be fixed.