All 'interesting' theories are possible, until the lack of data indicates that they really are not likely
This is exactly the point. In order to exclude a theory, you need to exclude all possible choices for the parameters of the theory. And this is what is complicated: Some combinations may be excluded... Excluding all of them is however a more complicated task. However, when one is left with only extreme parameter choices, we may lose some nice properties of the theory... and then give up and focus on more interesting frameworks.
[...] but failing to find anything where there should have been something, you move on to explore more likely theories.
Here, the point is that we only be able to push the frontier where the something lies a bit further. We can only say that there is nothing, up to a certain point, with the new phenomena lying potentially beyond that point.
Yes, you can call me a dreamer. A dreamer happy to share some pieces of the dream! ^^
Thank you :)