Please pardon me if I'm misunderstanding this.
Tor connection profiling, as long as I've understood, may happen when you visit clearnet sites through the TOR network, but not when visiting onion sites (because you don't use an exit node). If this really is the case, wouldn't it be a good idea to remove the clearnet home page from the default browser in Tails? The way it is configured by default, you always send at least a few clearnet requests just by opening the browser, which could allow for profiling. Isn't this a definitely insecure setting?
Again, pardon my ignorance. I'm trying to learn :)
Traffic profiling can be done for hidden services too.
If it travels across the Internet, it can be profiled, Tor or not. The only things that can't be profiled are things on your own network (unless you are profiling your own network)
But these profiling attacks have an ultra low success rate. < 5%