New players start at 1500 PSR, however in many cases they are nowhere near that level in ability or skill. I feel that new accounts should start with a lower PSR at roughly 800 or so, this gives them players who have little experience or are less than adept at some heros. This would also solve the issue with match making being completely offset by a fresh 1500 being drafted to your team. They have no skill and no idea how to play, but they can possibly take the top slot in a mm game, causing the other team to have a significant advantage.
You're assuming that 1500 represents an absolute level of skill. Not only that, you don't give any indication as to how changing it to 800 will actually affect the system.
You should read Michael Burge's PSR thread in the Mechanics section(here), where he outlines many of the issues with the PSR system. Your complaint is not one of them, and isn't a real issue. And before you start suggesting grand sweeping changes to the PSR system with no real clue how they'll affect things, you should at least make an attempt to read the work of people before you.
PSR should be removed imho. Having PSR when there is MMR is just bad as it does not add anything but confusion.
Ideally new players should only play with new players, so people have a more accurate MMR once you get out there among the older players.
Why not have it so that for the first match, your MMR/PSR adjustment is trippled, then doubled for the next 4 matches or so. Faster initial converge is crucial when dealing with both newbies and experienced MOBA players. It just gets more funfor everyone when the teams are even.