Over the years, what caused multi-day matches to massively outnumber real-time matches, which used to be dominant?

Real-time matches are still dominant, but they go through quickmatch now.

Quickmatch is what directly killed the real-time lobby. The multi-day lobby is more resilient, because if you play multi-day games you're not in a hurry.

It's a shame, because I really liked playing real-time games on interesting maps, or many-player FFA's, which quickmatch can't offer, but alas.

indeed, it is sad. I remember when I first started playing the game, I only played quickmatch, I guess because it was right in your face.

The simple answer is this: MD is just more convenient, logistically.