The theories that are powerful and worthwhile are the ones that are rarely or never wrong. Can't always get "never". It's a complicated world and we aren't all physicists. But we at least ought to be able to get "rarely", and if you can't, well, I guess it's not science then. That's OK. Unfortunately, not everything is amenable to science, though you can still approach it in this spirit of trying to see how you might be wrong rather than proving yourself right.
Once you start looking around with that standard, it's not hard to see how little science is really being done. Why are we publishing these dubious studies? Because for all the scientific trappings we claim, with statistics and p-values and carefully-written recordings of their putative procedure written in precisely the right way to make it sound like everything was recorded (while still leaving out an arbitrary number of relevant details), we've created a system where we are telling people to look for reasons why they are right... or we won't publish their results. Guess what kind of results we get with that?
If you start from the idea that you need to look for why you are wrong, the scientific method will fall out of that, along with any local adjustments and elaborations you may need, and every discipline, sub-discipline, and indeed at times even individual experiments need adjustments. If you start with "The Scientific Method", but you don't understand where it came from, how to use it, or what it is really telling you, you'll never get true science, just... noise.
I share your worldview. Makes intuitive sense to me. It's intellectually honest. And if I'm wrong about something and no one corrects me, I get kinda grumpy.
Maybe everyone else already knows, but I learned relatively late that it's called Popperian.