Part of the reason for it being implemented via email specifically was unreliable and slow internet in the early days - properly connecting both players might not be viable in a lot of cases, but just sending along the data of the game state, and having players take their turn on their own, would be a lot easier. These days, most game companies operate on the assumption that everyone has a perfect connection (even if this isn't necessarily true, especially depending on where you live), which has also been used to justify the lack of LAN functionality in a lot of games, something which used to be pretty much standard for PC games (the actual reason probably has more to do with anti-piracy measures, but "surely you have good internet, you don't need LAN" is the publicly given reason at least).

Play-by-email itself is rather niche, since it's only really suitable for turn-based games, so that probably didn't do it any favors. You could likely improvise it in a lot of cases though, by just passing along save files manually (which these days is at least a lot easier to do, there's plenty of services for you to upload files to, and saves wouldn't really exceed size limits in most cases).