First of all, it's a licence fee (with a 'c') - the noun/adjective is spelled that way in UK English.
"But we have to pay again in order to watch a missed show (because maybe out earning a living)?"
Do we? I thought that the iPlayer was going to be a free service (if you happen to have a Microsoft Windows PC and enough bandwidth allowance) in the same way that 4OD is.
"Or is this "you should set your video"?, but then that's illegal too."
No it isn't. Time-shifting is perfectly legal. Keeping stuff forever isn't.
"I think they should offer this service as part of the the TV license (no price increase either) to at least make it value for money."
Which is exactly what is proposed.
"Then again, if you watched TV via the internet and had no actual TV receiver, I guess TV license wouldn't apply??"
Yes it would. A common fallacy. "You need a TV Licence to use any television receiving equipment such as a TV set, set-top boxes, video or DVD recorders, computers or mobile phones to watch or record TV programmes as they are being shown on TV." Look it up on the TV Licensing website.
"Anyway BBC, when are we going to get TRUE HD (1920x1080) digital terrestrial TV?? Or will that be subscription based too!?"
Interlaced or progressive? There's more to TV than pixels. And you should be asking OFCOM about that - it depends whether the BBC gets the bandwidth for it at an affordable price. You might not get HD of any sort on Freeview if it's all given to the highest bidder.
Matthew Marks