It should cease to matter once a match goes to extra time.

Although I should mention that Juventus losing is also one of my favorite things in sports.

And I thought that even before Liverpool's loss last year. It is one of the few things I think MLS had correct in their playoffs when they had two legged ties.

Each team got a full match to get an advantage. Yeah, the home team still has their supporters but all in all, if it goes to ET in leg two, advancing should be based entirely on winning outright.

The home team in the second leg either earned the right (finished first in group for round of 16) or "won" the draw (quarters/semis) to host the second leg. I think having ET at home is a justifiable reward for earning/winning the spot to host the second leg. Yes, a draw is random, but I think winning should be rewarded. With away goals counting in ET, the "losing" team is rewarded.

I do like your concept of having to win outright in this scenario. That actually means more to me than my convoluted logic, so I'll have to remember it if this ever comes up again.