Great topic!
I absolutely hate games ending with PKs/shootouts, especially late in state cups. It's akin to settling a baseball game with a home run derby. It's a different sport entirely and, as was articulated previously, just above a coin toss. It's not like anyone thinks the winner of PKs is the best, most-deserving team.
I understand the world cup argument -- if it's good enough for them, who are we to use a different system. But I understood part of this is pure exhaustion. WC have limited subs and no re-entry, I thought, so playing lots of overtimes might be difficult.
I don't know what the answer is, but I have criteria in mind. In other sports, the best systems are those that: 1) require the as close to the same skills as the game they are trying to resolve; and 2) where both teams get an equal crack it. For example in football, NFL is good on 1 lousy on 2 because one team might not even get the ball so the coin toss often has too great a bearing on the outcome. College football, I think, has it right: both teams get an equal shot on offense on a shortened field and after 2 sessions they must go for a 2 point conversion to reduce the odss of a tie. Baseball plays until someone is ahead after both teams have equal chances. The NHL does shootouts in leass meaningful regular season games, but plays OT in golden goal until someone scores, even it it takes the equivalent of another 2 full games. i think that is pretty good.
Using the above criteria, I would think a good system for soccer would: 1) still play soccer vs another sport; 2) play until someone scores; 3) give both teams at least one chance at the same direction; and 4) if possible, does something to decrease the chances of the thing going on forever.
I feel stronger about the criteria and that others will come up with something better than I could, but if you forced me to invent a system:
I would then favor 2 10 minute silver goal periods, then as many 10 min golden goal periods as needed, switching ends. I would favor dropping 2 players (or other ideas) that would increase the chances of scoring begining with the 3rd OT because we have to face the reality that there is usually someone waiting to use the field so you can't have a 5 hour match.
Just my 2c