Not to argue, but to discuss -- trip relays are in EM games for that purpose. They are 'hit a thing and remember' relays rather than quick pulse 'increment a counter' relays. Late 70's games with multiple players removed ball-to-ball memory, but there were a few decades of EM games that did contain memory.
With regard to 'qualifying' the playfield - some EM games did exactly that. In fact, most late EM games have something called a 'ball index' relay (to pull from the Williams manual). This relay will not change state until the playfield is qualified. If the player manages to lose their ball without this relay changing state, the ball will be returned to the player without incrementing the ball count unit. This, however, is not a trip relay - it's a pull and hold relay.
And... of course... my favorite type of game has the best example of EM memory. Bingo pinballs had not only ball to ball memory, but game to game memory. Things like carry-over features and the reflex unit would influence the /next/ game. Think of how difficult it would be to count the number of balls shot while still allowing balls to return to the player. Then add on top a variable number of extra balls that can be awarded. EMs are capable of incredibly complex computation if they are designed that way.
Thanks for the show, more pinball talk is always good. Just reading the thread here, so sorry for the post replying to an ancient post.