I wouldn't say 23 rads is that excessive - I live in a modest 3-bed
detached and that has 13!

It could be that the radiators are sludged up at the inlet - in a
previous house, I had large double rads that didn't heat up until the
heating had been on for hours - they were almost cold to touch at the
inlet, but the pipe was very hot. They were sludged up quite badly -
after remvoving them and hosing them out we found they heated up to a
good temp.