Either someone would retrieve the cleats (me, DH, grandparents, another team parent) and would get them there before the start of the second game, or they could borrow footwear.
If this were my family, there wouldn't be the retrieving part--there would be a prompt before leaving the house, but no parental scramble to fix the situation, not for an extracurricular activity. Borrowing shoes is itself a natural consequence (ew, plus they won't fit well).
But only you know what works for your family! If this is really OK for you, DH, the grands, etc., that's yours.
We have made more effort to "fix" things that WE think are important, like retrieving the homework paper he left at school *with him* (not retrieving it for him). Our feeling was that in elementary, if he left the paper at school and undone, he would get extra free time (because less homework) and be allowed to recognize that it wasn't that important. We chose to cultivate the feeling that school is very important, even though it was inconvenient for us-- and the natural consequence was that he lost free time in going back to school and retrieving the paper, as well as then having to do the homework.
We tend to think it through as "is the right behavior being rewarded?" We try to set it up so it's really easiest and most pleasing if they do the right thing.
