There's no technical reason why iPlayer can't work for me, and I'm perfectly willing to pay a subscription if that's what it takes...
Correct, there is no technical reason. However, it would be a significant risk to the BBC to launch a subscription service for content.
Risk #1 - If subscription works, the UK public might, quite rightly, tell the beeb to jog on come licence fee time. The BBC know they have a bias problem, and that is why they refused to publish the Balen report, but they persistently refuse to address their problems - why then should anyone be compelled to pay for BBC if they choose to watch Sky or ITV / others instead?
Risk #2 - If nobody subscribes, it would evidence that the corporations best days were truly behind it, inevitably leading to calls for a signficant reduction in both the licence fee, and size of the BBC.
In the interests of full disclosure, I love the BBC. It produces/commissions a great many high quality programs. However, I stopped consuming any and all forms of BBC news a long time ago, after reaching the conclusion it was more or less Guardian TV, with echoes of Pravda.
 The Guardian: Wrong about everything, all the time.