Allow (trusted) people to accept new users with their invites
This coincides with #589 and is the 2nd part of LukeZaz's comment which I think is another good suggestion:
Allow existant users to accept the above-requested invites themselves by consuming one of their 10 invites, OR give trusted users the privilege to do this (similar to topic title editing / tag editing / moving). I don't know how many requests you get by way of email now, but given how much else you do to maintain the site I'm nervous about the idea of increasing the workload here. Letting other users accept these invites would both help them get on the site sooner, and also help you avoid having to manage them all yourself.