"Why did you make them wait all bloody day for their presents??"
You might as well say 'why did you make them wait all bloody month for their presents'
- because you do 'make them wait' all through December, don't you - and whatever time they have always opened them seems absolutely normal to them, as all families make up their own traditions.
When my children were young, they had a well-filled stocking from Santa first thing in the morning which had to be shown around once the adults were up, and each item examined and exclaimed over.
Chocolate coins and clementines for breakfast, food preps, carols on the radio, much bustle and excitement, TV on for festive Christmas colour. Lunch with the whole family sitting round the table, crackers, etc.
THEN when all is cleared away it's Present Time.
We always thought it by far the best and most fun way to do it, as it makes the whole day full of one exciting happening after another, with the present-opening the last and perhaps best thing in a day of good things.
OP's solution of waiting till 12 seems absolutely fine to me.