I don't think the lack of ties is what makes the NFL's tiebreaker system so bizarre. What's driving that is an expanded league with imbalanced schedules, many divisions, and multiple wild card teams in the playoffs. You're starting to see a similar issue creep into MLB in some seasons now, too.
Americans and Canadians really get a rash from ties. Most of the rest of the world is OK with them.
The tiebreaker system in the NFL is crazy because with a 16 game season there’s just not enough variants in results. Without ties there’s only 17 possible season results with 32 teams your guaranteed ties in the standings so then you need ways to break them, and with a league where everybody doesn’t play everybody you need to start digging into odd stats (and eventually a coin toss). If you add ties in (I’m really for no regular season OT) and a “normal” point system (2 for a win 1 for a tie, 0 for losing) you get 33 possible standings results and the actual numerical possibility (though not exactly likely) of no ties. You also get an additional tiebreaker of wins over ties.