In Canada, CBC Radio One is a mix of local, provincial / regional and national, depending on the day / time.
For example, the only 'local' shows in Newfoundland and Labrador are the morning shows: St. John's Morning, Labrador Morning, and CBC Newfoundland Morning (which covers Central and West-coast Newfoundland - this is a merger of the two previous shows for both areas). There are province-wide shows, such as The Broadcast, The Signal and On The Go, and then the rest is national. There's a couple of regional (Atlantic) shows at the weekend too, but these are generally to cover the fact that the Atlantic and Newfoundland time zones are behind Eastern and therefore have 'time to fill' when joining network.
It works well, and is a pretty decent listen through the day. But it's not the same in other provinces and territories, with some having more 'local' shows to suit different areas. CBC Radio One in Quebec and NWT are good examples as they have splits to suit indigenous communities / areas. A nice table is listed on Wikipedia:https://en.wikipedia.org/wiki/CBC_Radio_One#CBC_Radio_One_stations
For me, as much as I'd love local shows on BBC Local Radio to go back to how they were (the 2006 re-launch of BBC Radio Manchester being a personal highlight for me - bold, big and very local), it's not going to happen. I think the best plan now would be to move towards the CBC Radio One model: i.e., merge BBC Local Radio with Five Live and put the resulting station on the FM local frequencies in England - have local breakfast, lunch, drive shows and local sports or other local shows when there's no local sport. But also allow the local managers to make the decisions on how local to be and when, within reason. Take Five Live off medium-wave where possible (or make it entirely DAB in Scotland, Wales, NI), use the cash saved from that to plough back into the local aspects of the new stations and make them as good as they can be.
And they need to re-vamp local news on the web - BBC Manchester's 'Local Updates' section (
www.bbc.co.uk ) is 90% sport (and 80% of that, at least, is football), and has been for a long time. I'm not interested in sport so it's not for me, and a mess to pick out the non-sport stories, As much as I get the arguments from both sides surrounding what role the BBC should play in local news, they could do better even within a limited remit. Other areas may differ, I'll be honest and say I don't know.