Now, “falsification” itself is a silly/naive cartoon-ish framework for how to do science. It has its uses, but we mustn’t cling to it too much (which would be cargo culting). We certainly have many other useful approaches as well.
In fundamental physics, unlike models of other limited domains, experimental results/constraints over history keep composing on top of each other. So, it is very hard to build a theory that satisfies every one of the past constraints. In a sense, string theory is the only example we’ve managed, on that front. Other “alternatives” consider a much more limited domain (quantum gravity), for better or for worse.
Whether we must continue investing effort/resources on that front is a political question, not a scientific one. And that is a complicated question, with many aspects to consider. Let’s please not get hung up on the “falsification” bugbear. If we were really nitpicky about falsification, we would completely cease doing/studying/researching psychology, economics and a whole host of complex topics.