Hi Whopity,
Agree wholeheartedly for first solo (although that should be obvious) and for next few solo hours. (although i suspect we have confusion over the meaning of "sending solo")
Towards the end of solo consolidation - or solo cross-country - then recency rather than immediacy is the key. If they can land at another airfield and then take-off again to fly home, no need for an instructor to check 'em out.
Does need to have a relationship with the student, be able to ask them how they feel and be able to check body language so as to cut through bravado.
As Whistler said when defending himself in court from Oscar Wilde's accusation that his painting were mere daubs of paint and no more than a few minutes work: It took a lifetime to learn how to do it in a few minutes!
That's why continuity of instructor is so important - assessments (such as later solo flights) can then be made in a shorter period of time, and by doing so help boost the student's confidence. (or not destroy any fragile confidence that has been built up).
very best,
XA