Other competitive games already do this, although some via third party services. For league of legends, several websites (such as OP.gg) have recorded games readily available for most of the high level games played during the last few days, that’s also true for rocket league (through sites like ballchasing.com), etc.
Voobly has been doing this for years and no one has ever complained about it. It is a great feature for people who can’t watch their favourite players play live (or can’t find the games being played in the currently incomplete spec tab) and want to learn from their games.