I have a great reason for it. There is literally no reason for them to do so, the technology has already been implemented. It would be a huge time and resource investment for them to create something that already exists for players to use (curse voice). So if I could be allowed a question to you, what is stopping you from getting a curse voice call together with the random people on your team?
First of all, you are assuming the League client can handle a voice chat; its 5+ years old and when it was created it wasn't made in anticipation of what this game would become. For example, a few years ago Riot had to increase their number of servers to handle the number of people playing the game.
Also, the same problems would exist for a League voice chat; You are assuming that everyone is going to have mics for it and that everyone is willing to go into a voice chat with people. The thought process that some people can talk and others can't doesn't even hold water because, of course, the ability to mute people would still be an option. So, why should Riot create a system that already exists and will have the same problems that an existing system has? They gain nothing from it. It would be better for League to "endorse" curse voice and get more people comfortable about using that than it would be to create a whole new system.