Or free throws.
It is interesting to get different perspectives on this. I played on/off for ~20 years, with a modicum of skill and buckets of enjoyment (save for indoor, or artificial turf/green carpet - a pox on that stuff). PKs are part of the game, but it's largely one in which the test of skill is a test of the propensity to commit an unforced error. If you shoot it hard enough within 3 ft of either post (interior side, obviously), it's going in, unless the keeper guesses correctly (and moves early).
Anyway as someone who played a bit, it's interesting to hear about claims of cruelty for the poor tired players. I wonder if they really feel that way. A full sized pitch is enormous and there are 11 players a side. Not all players are continually running, but some run more than others of course. And I say this as a defender, so perhaps I am too ignorant of greater distances put in by forwards and wings.
I hadn't previously commented on substitution rules, but yes, they seem to me an excellent option for mitigating team fatigue. A great liberalization of those rules would be fine by me, especially since they don't fundamentally alter the play. I would be in favor of hockey-style substitutions, that is, eliminate play stoppages due to substitution which are characterized by a slow walk off to the sideline and then greeting the sub who can finally enter after you slap their hand. Make them run off during play and go a man down momentarily, and then the new player enters. Note: by hockey-style, I don't mean by that entire "lines" of players that come, go, and come back. I'm not against it, I just don't know that can really apply to soccer.
As a bit of a purist, I would prefer a solution that involves a tie being broken by a goal in the normal course of play, not PKs. That said, what about the size of the goal? Has it not been the same for over 150 years? Haven't Englishmen gotten larger since then? Not to mention selection effects for professional players. So increasing the size of the goal might be another possibility. Heck just "keep it" as 8 x 24 (2.67 yds x 8 yds) but go to 2.67 x 8 meters! 20% increase in goal area. Move back the PK spot if necessary to balance this off a bit, but based on the 60 and 40 percent success rates in the recent Euro final shootout, maybe that's not even necessary!