So basically we agree then. I brought up string theory for that exact reason you stated and I'm glad you did. It's mathematically sound and gets more testable all the time but is not there yet. At the same time many aspects of parapsychology advance the same way but for some reason still get shafted. The reason websites like "Skeptiko" exist is because people of all avenues who wanted to study this stuff started standing up to the mainstream dogma, and it really is just dogma, that "it's all bunk" and went "where's your evidence for that?". Increasingly it's turned out that the mainstream didn't actually have any, they've been talking out their asses because of prejudice.
Dr. Rupert Sheldrake has a good Google Tech Talk about his own research and flak he's gotten for it for example. His dealings with James Randi and Richard Dawkins are especially hilarious and enlightening. Dr. Jack Hunter, an Anthropologist who, last I checked, is studying why ritualistic methods developed along side mysticism with the hypothesis that maybe it's because they just plain work has other interesting things to say on the topic. IANDS the International Association for Near Death Studies is another. Dr. Ian Stevenson being I think one of the first people to try studying Reincarnation claims seriously, People such as Dr. Erlendur Haraldsson continue such research.
There in fact have been more testable experiments for psychic phenomena for much longer than String Theory, math to back it up and theoretical frameworks for them to fit into, and evidence than there was for String Theory during the same time periods but String Theory is accepted as science, not psi. It's like how Aristotle claimed large rocks fell faster than small ones because they felt heavier. But he never took 5 minutes to test if that was actually true. But his claim was considered fact all the way until Newton except maybe a few "crackpots".
In the same way common sense claimed that if you feel someone is watching you from behind and you turn around and see someone and you think it's because you sensed them, it's just because of confirmation bias. Same with knowing someone was going to call you before they did aka telephone telepathy. But the mainstream never went. "Hey let's test this, let's sit someone down, we'll have someone either watch them or not, and see how accurate these people are with tier feelings. They're either right or their wrong, 50% chance levels per test." Very, very easy to test and has been testable for most of human history.
This is probably why it's an important practical part of higher levels of martial arts like Kung Fu because being able to accurately "feel" an opponent you can't see gives you a definitive tactical advantage in a life or death situation. Some such as Sheldrake argue that psi abilities may have evolved as part of the predator/prey relationship. Psi has in fact been more "scientific" than string theory for a very long time. It turns out that people can in fact quite reliably tell if someone is watching them or not, same with telephone telepathy. But still to this day, despite all the trials and evidence, it's still not accepted as "scientific".
But all of that and the increasingly large amounts of evidence is not at all what's pushing the change in perception. It's the debate that is. Popping the assumption bubbles that the alleged rationalists tend towards and sort of rubbing their noses in it. It's one of the reasons I argue that it's not mathematical concepts like scientific method we need to start with, it's self respect and more feeling based things.
This is because the evidence shows that emotions matter way more to peoples decisions making process than logic. So that's what should be tackled. The idea being that if people feel good about making mistakes as a process for learning because they logically understand why they actually make them more accurate they will sort of derive scientific method themselves or be more likely to stick to it more strictly without straying.
::EDIT:: I'm sorry if this seems like a really long rant. I was just trying to support what I was saying with logic and some evidence.