In some respects it's a great idea, but in others it would be a nightmare.
Maybe, as someone else suggested, flash inspections could be done with no notice, but the more indepth inspections done with a couple of days notice.
I'm a school governor, I also have a job, children and a million other things, I can't just drop everything with no notice. Would lack of governors involvement during an inspection risk the school being down rated? If so, it's totally unreasonable to drop that on a school with no notice.
When my school had its last inspection, the inspectors expected a lot of the governors, I was in school for a whole day, I had 48 hours notice to arrange childcare/swap work days/change meetings. I couldn't do that with no notice.
Also, what about stuff like whole school trips? Development days?
Our last inspection had to be delayed by a few days as the school was closed for development days due to moving. Thanks to our twatty council and their inability to organise a piss up in a brewery, we had 4 days to pack up and move schools so the head added 2 development days. If Ofsted had just rocked up with no notice they would have found a packed up school with no pupils in it