What if the maximum size of the sideboard was determined to be 1/4 of the player's deck size instead of being 15 cards?
(Of course, Limited should still allow sideboards as large as the players want provided they make a 40 card main board.)

All sideboards would remain 15 cards.

But if I bring a 100-card singleton to FNM, I would be able to have 25 cards in my sideboard with a 25% sideboard rule.

I think I was talking about a rules change.

Did Wizards really put a limit on deck size too? Like, you must have a deck of 60 cards?

There's no limit, no. But it'd still be optimal to make your deck the minimum size allowed. In practical terms, you'd hardly ever see anyone taking advantage of the sideboard rule change.

No, I think what Lily is saying is that all practical and competitive players realize that maximum consistency is gained by busing the absolute minumum allowable number of cards, and as a result at a competitive level, people would never run 64 card decks just to have a sixteenth sideboard card. Anyone remotely competitive would still be running 60 card maindecks and 15 card sideboards. This would be a rule change that serves no actual need and would have almost no relevance. They're not into muddying waters with rule changes for no relevant benefit.

To be honest it would be a boon for those janky decks that use Battle of Wits. But that's marginal.

this could theoretically give you an incentive to bring a larger deck, because you could then pack more silver-bullet answers and have options against a wider range of opponents, but I doubt that outweighs the consistency gained by going 60-15.