it's not that simple tho
like, it's pretty obvious that replays should be a thing that exist in this game but it's not something so trivial, specially the way riot wants to make it
basically the big issue i see are patches. patches change a lot of stuff, including number balance, art and sound assets, the layout of the map itself, entire game mechanics, runes and masteries, etc. etc.
so how do you allow ppl to watch replays from last patch? well, you basically have a ton of servers hosting the game at every possible patch so that when you want to view a replay from 5.12 the server just gets asked for that, downloads the assets and plays it in "5.12 mode". this to me sounds kind of nightmarish since you're essentially supporting like a million different patches at once and you have people downloading patches all the time, plus who knows if the game would actually support this stuff, specially since patches have bugfixes so if you got kliled because ap ezreal procced luden's echo in 5.12 then you have to reintroduce that bug in the replay for it to work. riot on top of this wants to store all replays server side for some reason which is cool and i'm guessing it's not what's stopping them from actually pushing replays to live since they could easily just store replays locally while they figure out the logistical hell that it must be to store billions of replays for 70m people
and you can really see where the 3rd party programs cut corners to do replays, with their shitty interfaces and crashes and replays not recording or not working and not working anymore after a new patch comes through.
but yeah not having replays at this point is pretty inexcusable, i'm sure there are books written on how to do this kind of stuff and riot engineers who are much better than me at programming have probably read them all, so i'm not exactly sure why they're taking this long. yeah it's probably a pretty difficult thing to do, but it's clearly possible as other developers have done it