The general consensus seems to be that the away-goals rule is bullshit justified only by the fact that penalty kicks are worse. I would tend to agree with that but still can't help to think that there has to be some better way. I know that the threshold for neutral-ground tiebreaker games used to be a lot lower in all competitions. In the old days, for example, when the Champions League was in its true form as the European Cup and only national champions got in, the tournament was small enough to have a third game if teams were tied on goals after home-and-away. I do realize that the schedule has probably gotten too heavy for that, and I know that the Champions League isn't going back to what it was. The current format is geared towards an international audience who only recognize major names and UEFA isn't going to risk the loss of treasure that unfamilar cast of characters wold bring. But I guess that's a completely different issue.
If the sporting ideal meeting halfway for a third game isn't viable there are still other things that could be done. In the CL round of 16 it would seem a very simple matter to settle aggregate draws in favor of the team that topped its first round group. This would have the added blessing of rewarding teams who come out from their own ends and play to win much more then the away-goal rule does now. As for later rounds; well, surely the underlying principle should be that all available means to produce a team that truly won by scoring more goals than the other must be used, and that all other sporting concerns are secondary to that. What this means first of all is that extra time should always be played when teams are even after 180 minutes. True, this would give the team that hosts the second leg an unfair advantage, but this could be compensated by deciding a match that remains tied after extra time in favor of the team who had to play more ball in front of a hostile crowd. I know the obvious effect of that would be for the away team to barricade themselves in front of their own goal while the home team tries to tear through them. Some might think that would be too ugly, but I think it would work. It would be a concept similar to the 'clinch' tiebreaker used in international wrestling and could produce some real classic trident vs. net style competition.
The second thing that should be done is bringing back golden goal. (Sudden death for folks here at home) This was scrapped on the idea that having a chance to come back is a sacred ideal but I don't buy that myself. Game winning/losing goals in the last minute of injury time are already a thing that happens so I can't get behind the idea that sudden-death ET would be some alien distortion of the game. I suspect that the real reason golden-goal was scrapped is that an unknown end point created the possibility of having subs on the bench that could have been used and making the losing manager look bad. And of course the national treasuries worth of money at stake in this game is the most obvious reason for a general 'conservatism' all around; 1-0 hammerfests on the field and bureaucratic stuffiness in administration both alike. But this again is a totally different issue.
My last suggestion is I admit at least borderline crazy and one I consider optional, but why not keep going if still tied after 120 minutes? I realize that baseball-style 'play till you win or die of old age' isn't viable That if you went on for too terribly long past the two hour point players would literally start to drop dead, and that would be bad. Then again, this is the continental championship, UEFA already has that godawful 'anthem' , not theme song but "ANTHEM' to hammer home the point that you are watching The Epic. Why not just one more half-hour of play to try to produce a real winner, maybe add an 'automatic red card' to make it 10-on-10 on top of that, if that's not too American for you.