I'm not looking to debate it, but your subscription fee for BBC America doesn't contribute to iPlayer. It is just paid for Discovery to licence the BBC programmes it shows.
There is also licencing issues, BBC America only showes a small selection of the programming from BBC 1,2,3,4, News, Parliament, CBBC, CBeebies, S4C, Alba, etc. But also gives you programs from non BBC UK channels. So providing you with access to iPlayer requires further work to limit you to the small selection of programmes you're allowed. I understand you can still access the BBC radio stations in the US online.
The main issue is that BBC America is essentially not a BBC channel. It is basically like any other US channel provided by discovery but with BBC branding. It is part owned by BBC but that's as far as it goes.
So your point is the same as saying, "I have an iPhone that can open MS office documents, so why cant I have Cortana" They're entirely different services provided by different companies, and you pay for one and not the other.
Having two otherwise identical Lumias and one can do it whilst one cant.