I don’t think a subscription model would ever work for a national broadcaster of lineal TV.
The big question becomes "why"?
If eg not enough people would subscribe then maybe that means it is dependent on contributions from people who don't watch.
Commercial channels manage OK so why not BBC?
The trouble with paying from General Taxation means even more people who don't use BBC will be paying for BBC - so in many respects worse than current situation.
Maybe I don't understand what a "public service" broadcaster is, what it means and why or who needs one. According to UK Government this means "
Its main responsibility is to provide impartial public service broadcasting in the UK, Channel Islands and Isle of Man." but then other channels have the "impartial" constraint as per OFCOM (eg Channel 4).