Here's how my understanding and/or perception of the BBC Three story goes...
The station's initial launch was much-delayed, and I believe it was ultimately only just about approved by the-skin-of-its-teeth (by the BBC Trust/Ofcom/government/whoever's place it is to "approve" these things). So, presumably the proposed "yoof" remit was regarded as a questionable use of licence fee money? Or something?
I myself may or may not have been in the station's target demographic at any point during its existence to date (I'm currently 35). But, even if I was/am, my viewership of the channel has been infrequent at best.
My (admittedly perhaps not best-informed?) perception of the channel's content is that it's often been stuffed full of endless back-to-back runs/re-runs of things (e.g. endless Two Pints in the early days, endless Family Guy* in a more recent era, and so on). (*the latter also being a US import show, rather than original BBC-commissioned/produced content).
Considering the station's already relatively limited broadcasting hours (evenings and overnight only), by the time you take out all of the back-to-back repeats and/or imports, I'm not sure that there's *ever* really been enough fresh original content to justify a whole actual channel in its own right (not even an "evening only" one)?
Yes, some big popular cultural successes (e.g. Little Britain) were born on BBC Three. But, in an alternative dimension where BBC Choice/Three (and BBC Knowledge/Four?) were never invented, it's perfectly plausible that programmes like Little Britain would have been commissioned by BBC Two - the channel that gave us the very anarchic The Young Ones, for example.
It has oft been said by various people that Three and/or Four basically took different elements what Two used to do in days of yore, thus leaving Two rather struggling to find a purpose. The reason it's been oft said is...
because it's true!
Spreading essentially "two channels' worth" of content over three/four channels, makes about as much sense as a vegetarian butcher.
So, I for one applaud the closure of the BBC Three television channel as utterly sensible.
If you want an innuendo, I'll give you one.