I am finding the stances taken by both sides to be genuinely intriging.
Personally, I would have preferred no visitors for the first day with DC1, as it was a section, and I was not feeling well. (I threw up all over the bed when the ILs arrived for their visit, but MIL is so very practical and helped out.) After that it was fine, but really the first few hours, I could have done without visitors. Especially as I so badly wanted sleep.
For DC2, I gave birth naturally at 11pm and was home the next day at 1pm, so less than 24 hrs. No time for visiting in the hospital, which was 20 miles away from home anyway. As my parents had been looking after dc1, they collected her from nursery at the usual time (she was 3.9 yrs), and also collected my MIL (FIL having sadly died between the 2 dcs) and everyone came together for that first visit.
My mum was not present at either birth, and I know she would not have wanted that, despite our very good relationship.
Luckily my parents and MIL are the type to make those short visits and don't hang around. They came, cooed, hugged me, had a quick cup of tea made by the other half, and said their goodbyes. And left us a few days to settle. Great!
But I can see the other side. When in hospital after both births, I saw new mums being overwhelmed by visitors, and in some cases it was clear both mum and baby were distressed. That isn't good, and people should remember to be considerate when visiting.
Different people have different background and personalities. What suits one family or person may not suit another, and this should be respected. I think the OP is not BU for wanting to visit, but a delay of just a few hours surely should not be considered outrageous