In a sense, yes. It could conceivably be transformed into a publicly owned, not-for-profit, subscription service, retaining BBC property, including its intellectual property, its studios, technology, its staff, and so on. But really this would be such a fundamental transformation that it would hardly be the same organisation. Different parts of the BBC at present do serve particular subsets of the population in terms of geography and demographics.
But its overall domestic operations have always been defined in national terms, with universal access being a founding principle. Unlike commercial media – whether subscription or advertiser based or both – the BBC as presently constituted doesn’t have an economic interest in targeting wealthier groups. Everyone who watches TV pays the licence fee (bar some exemptions), and in theory everyone is therefore equally important.
One can of course query the extent to which the ideal of public service broadcasting has been realised – I certainly do. But in any case, a shift to subscription would be such a fundamental shift that the BBC would arguably cease to be the BBC in all but name.