The BBC didn't plan Youview to become a competitor to Sky in paid-tv. They feared, in a fragmented landscape, BSkyB could use their install base and financial clout, to become the defacto standard for IPTV in the UK.
Until a few years ago, Joe Bloggs seemed to believe that you had to pay BSkyB to receive Satellite. You didn't, but people would still buy a subscription to watch the free channels. Or you would have to buy a sub to get access to a decent PVR with 7 day EPG. It took the BBC & Co launching freesat to finally fix the issue.
I believe Youview was born out of the same mindset, but rather than trying to fix a broken ecosystem, make the right one from the start. That BT and TalkTalk have been able to use Youview so successfully is a consequence of the fact they got it right in making the platform workable for both free and paid content. The TV brands are still dicking around with incomplete propriety systems that fail to offer the full menu, and Sky would try to lock everything in to a sub only ecosystem.
People talk about BT and TalkTalk hijacking Youview, but they've ensured it short-term success and in turn that actually benefits those after free IPTV. The boxes aren't cheap but the BT/TT sales will help obtain economies of scale, supply a second-hand market and maximise the chance of other content providers joining the system.
The area where Youview does need criticism is failing to get any of the TV manufactures on-board. IMO due to being too strict about the Youview experience and not coming up with a version of the specs that the TV companies can bolt on to a TV.