Stags shot by clients are normally mature stags so will have had several years of leaving his genes, there are traditional rutting corries, where hinds gather the mature stags in good condition will be first to start rutting and make their way to the same corries year on year, so there is a very good chance that a hind has been lined by the same stag several years running.
A stag even one in prime condition will not hold his harem for the whole of the rut a good stag may start of with as many as thirty hinds , but that number will be eroded as the rut progresses, hinds being pinched from him by opportunist stags, but the fact of being constantly on the move ,sleeping very little if at all not eating all take there toll, even a stag in his prime will only last so long maybe three weeks absolute max before he is driven off where upon he will probably head of to the wintering ground to recover.
Much is made of good stags, but a good stag is only half the the story, you need a equally good hind, much harder to identify to produce a good youngster, why do people think its all down to the stag.
Early in the rut as I said its mature stags in their prime that hold the most hinds , this is not always the stag with the biggest head, so I would suggest from that there is more to being a good stag than just the size of his head.
In fact I would say that the food available has more to do with head a stag has than any other factor, there have been plenty instances in the past when park deer have been released with the intention of improving the quality
of Highland deer, has it worked not really in fact in a few years your park stag will have degenerated and probably carry no better a head than many of the resident deer.
Red hinds unlike Roe which tend to only come into oestrus once will usually come in again twenty one days later
by that time most of the big stags have finished so hinds that were missed the first time will almost invariably be mated by young stags.
When you take all the above into consideration I believe you are doing no great harm by shooting mature stags in the rut.