I'd miss it for local weather, traffic and the more important local news, and I appreciate that many follow local sports coverage too but I think much if not all of that could be incorporated into the national network with localised reporting (or the amalgamation of two or more local stations, as has happened in the past). This seems to be pretty much what they are suggesting. I'm not sure I'm convinced that the marriage of 5 Live and local is made in heaven, but...
Just under 8% of the BBCs budget is spent on local radio compared to 11% for national. Unlike, say dramas or BBC World there is very little scope for selling these services on so are unable to supplement the budget for their own or other output. According to the annual report, some £775m is generated from the commercial arm.
So in short, yes, I think its a very valid question to ask. If the BBC are spending a large amount of money on a service with limited appeal or revenue they should and must investigate ways to keep the "best bits" and localised public service broadcasting niches whilst reducing expenditure. They would be much more rightly criticised, in my opinion, if they continued to spend money on services just because they always have as opposed to ensuring that what they offer is useful, current and most importantly needed.