Indeed, because Kuhn and Feyerabend were reacting to very unusual times in the history of science where it was easy to get so excited about our new ontological understanding (in philosophical terms) that we forgot to pay attention to epistemology (which was basically unchanged).
I think you overstate how much Kuhn thought that paradigm mattered, but I'm away from my library right now so I can only provide an impression, not direct quotes.
The bottom line, though, is that the ontological revolutions in physics--the re-imagining of what reality "really" was, in a sense--were in fact tweaks at the edge of the coherent center, because science does not start with Grand Unified Theory of Everything and reason upwards from there; instead, it starts with the most blatantly straightforward observations, finds compact ways to describe them, and works outwards.
Aristotelian mechanics predicted very little (and it was obvious), and Newtonian mechanics predicted a lot more (also obvious)...and this was early when we were really just figuring out how to do science properly at all, so it's no wonder that our paradigms were all messed up. You can't reason about normal science in the time of Bacon and the Royal Society because there was no normal science--it was all paradigm-shifting!
After that, though, in practice we just haven't ended up with multiple incompatible paradigms wherein things only can be interpreted from within the paradigm and still fit observations. Physicists knew very well that there were problems with their theories--ultraviolet catastrophe, photoelectric effect, etc.--but they imagined that the solutions would be simple. Well, nope! But Newtonian mechanics still works brilliantly at the speeds and spatial scales that it always had.
Of course, if you have wrong theories, you can misinterpret your data rather badly. But this just takes you back not to Kuhn but to Popper or earlier: you test your ideas with evidence, preferably multiple different ways. If your theories are wrong, it's exceedingly rare that you won't have reality come back and tell you. For instance, you might note that violet light is higher energy than yellow, that things get higher energy when hotter, and that sodium turns flames yellow while potassium turns them purple. If you conclude that potassium makes flames hotter, you would, however, be wrong, and if you interpret more than a teensy bit of data assuming purple flames are super-hot and you can make your flames super-hot by adding potassium, you'll notice that nothing makes sense any more. So you have to go back and test all your assumptions until you find where you went wrong. This is just normal science. Heck, this is just normal logic. Finding a contradiction doesn't tell you which premise is wrong, it just tells you that you messed up somewhere. Usually the messup is small, sometimes it's big, and always the task is to fix the wrong premise--you just have more work to do when it was a big messup.
So I think Kuhn, in the excitement of the day, overstated his case (though he did add a valuable additional perspective); and I think you have overstated Kuhn. (Feyerabend I am less certain of. Some passages of his I've read gave me exactly the impression you conveyed, but others not. Read as "science is messy" he is correct--people don't only sit down and go, "Now, I have this well-defined hypothesis; let us try to falsify it!"; read as "science is undisciplined" he is not.)
In particular, the critical thing to notice is that almost all science is not theory-laden in a way that confuses you about whether your theory explains results or not. So you might think that the Andromeda galaxy is a nebula, but nothing you know about nebula formation is going to help you make sense of the distribution of or size of or appearance of or pretty much anything about galaxies. And that means that there is a very straightforward objective way to decide between theories: you throw out the one that's been most badly falsified, or the one that requires the most ad-hoc fixes every time a new piece of data comes in (if the proponents refuse to allow the falsification to stand and instead amend the theory).
Thus, although in principle we could end up with a morass of good theories which give us radically different perspectives on things, in practice we find that we end up with a morass of terrible theories. (This is not terribly surprising when you consider the space of all possible observations and the extraordinarily tiny slice of those that any decent theory will agree with.)
When you have only a morass of terrible theories, the correct approach is to say, "We don't understand this." You don't each interpret everything through your own terrible theories, leaving you mutually incomprehensible to each other. You just go, "Aw, heck, we're all wrong--let's observe more and think more." You retreat to the common coherent core from which you all started.
And when you finally find a good theory, the correct approach is to say, "We understand this to an extent--it works approximately like this." And then you try to find a better approximation--and at first all your "better approximations" are terrible at doing better, and the correct stance is, "We don't understand this aspect of the phenomenon."
The space for sociological factors to intervene is modest at worst. All that happens then is that everyone agrees that it is impolite to talk about how terrible the model is.
It's all pretty close to objective and impartial, in the ideal. In practice, people have trouble living up to the standards. But it's still objectively and impartially detectable when they fail.