The house private aspect can be controlled.
The house can be restricted after a certain hour.
This would be covered by saying, for example: Reposing at home between say
4 and 8. House private thereafter.
This would allow friends, family, acquaintances, TDs/Ministers habitual funeral attendees

)) and others to attend. Of course it would be good practice to allow flexibility in relation to the time. Some people are delayed. Others will travel a long distance.
This time specification will allow the family to get some well needed rest. (We are a business/farming family and a large family and live in a rural area and the 4 hours of non-stop hand shaking was exhausting, but we were very appreciative of those who came to say their goodbyes to my late mum.) We provided catering at home on the evening. We provided lunch for family, close friends and extended family in a hotel following burial the following day.
I would't have changed anything. Mind you it was all precision planned by the deceased who had a final week to submit her instructions to the family.
For myself: well things will be very different. But I'm not planning on leaving anytime soon.
Marion