Is there any reason why a linear BBC Three has to be broadcast in a conventional way? The connected TV streams on Freeview would probably do the job, capacity on other platforms is less of an issue.
As a totally non-reactive channel with pre recorded continuity it could probably wouldn't need a dedicated payout suite and team.
I'd imagine it would be that not everyone has the ability to connect their TV (or external freeview box) to the internet, and even if they can their broadband speed may not be sufficient. I believe the BBC aim for platform neutrality with the availability of their channels, which is in part due to being funded by the licence fee.
Whilst I think most could understand if a pop-up channel (e.g. BBC Glastonbury) was only available via connected TV, there would be a lot of complaints if a permanent channel was only accessible on Freeview if you had a reasonable internet speed. As a side-note could catch-up services such as iPlayer and Sounds be theoretically made available on Freeview via connected TV?
"Listen, we've all got something to bring to this conversation, but from now on what I think you should bring is silence." - Rimmer