When my daughters and daughterIL had their births, extras bodies was never discussed, I think I sort of knew each couple wanted to experience that magical experience together.
I had three out of four births on my own, and frankly I was happy for that situation, ---to me it felt right.
DS-- longtime ago you had a choice- first hubby screamish so discussed prior to labour and absolutely not for him, He was automatically gowned n masked up (Oxford Radcliffe) and when I saw him I said 'what are you doing here' I think they thought they had bought the wrong hubby in!! He was very happy to leave, he probably would have fainted if he had been present.
First TwinD --- 2nd hubby present --second one he was not allowed to stay! Not a pleasant labour for me but I still preferred to be on my own.
Sadly the first and stronger twinD died of SIDS 8 weeks later.
Last one-- DD, a week away from expected date it was DH aunts funeral, I said go to support your widowed mum, he left Sunday night to travel 3/4 hour journey. Early next morning I went into labour! and DD born before lunch! He did not see her until the end of the day.
So DH never saw his two surviving daughters born, but for me personally it is a very private thing, so I believe it is not a 'spectator sport'.
I wonder if there are other mums like me ---happy to labour on my own, and Dads who do not wish to be present either?