Don't get me wrong. I'm fine with transformations if you have a reason for them or they're appropriate for the type of data you're working with. But transforming just to achieve normality is silly to me. If you're doing that then why not just directly the model the data you have with an appropriate distribution? But transforming and then doing some sort of test is not a good route to go in my opinion. Typically the interpretation of the parameters of interest aren't the same once you transform the data. Heck sometimes its hard for me to understand what the parameters you're estimating actually represent once you transform the data. I don't mean to sound pompous but if I have trouble understanding the meaning of the parameters once you transform the data then I sure don't expect most people to understand what the parameters actually represent.
There are all sorts of tests you can do. Why force your data to meet a normality assumption when all you're really doing is making it sort of look kind of normal maybe and then applying a test appropriate for normally distributed data. If you don't think the data is normal then do a nonparametric test. Or do a randomization test. Or model the data with an appropriate distribution. But it seems like "it's the only thing I know how to do" is the only actual reason people resort to transforming the data and doing a t-test.
Why are we doing "back up" tests? This sounds like you're saying that if we can't find signficance with the test we thought was actually appropriate for the data then we should just try this other test and maybe we'll find significance? That sounds a little like fishing to me. I'm not a fan of fishing.If anything, that thing could serve as a 'back up'-test to your other tests that u perform.
But I agree, you should not perform tests on tranformed data unless it is really necessary.