The thing about that first solo flight that hasn't been mentioned on here yet is it's a confidence booster. The fact that one has flown an aeroplane entirely on one's own boosts self esteem and belief in one's own ability in a way nothing else will. This can greatly increase the rate of progress post solo as a result.
So as soon as a student is consistently safe it's surely a good thing to send them off solo and not wait any longer.