I can understand why BBC Three attracts some derision, but it has been a good ground for developing many programes that wouldn't have likely got a chance to develop on BBC One otherwise. Some of BBC Three's output has been dodgy, but that's the risk of some of its experimenting.
There's number of problems I see here. Taking the channel online only has a risk also of setting a precedent that further BBC channels may be shunted to online only in the future on the grounds of cost cutting. This disadvantages viewers and consequently licence fee payers who don't have internet access - or whose internet link isn't up to carrying streaming video either from bandwidth or data caps - whom won't be able to view programming that they have helped contribute to, threatening the universality of access to BBC's content. Secondly, a lot of PSB's worldwide have been accused of skewing program output towards older demographics and neglecting young adults. BBC Three nicely fills that gap for them. Third, in terms of capacity made spare, CBBC will still remain there until at least 7pm I would assume. On Freeview this would leave on SD & HD part time stream blank in the evening, and it would seem ridiculous just so soon after launching a HD stream to suddenly abandon it. I can't imagine that the distribution costs take up a lot of the budget for the channel anyway - if they're going to move the channel online presumably most of the production costs will still remain. What I would look at is the BBC Two costs, it certainly doesn't look like a channel that has over £400 million spent on it a year, not to mention that it seems to have a bit of an identity crises. Maybe it would be better to merge BBC Four into BBC Two to give a single high-brow educational & entertainment channel with a strong budget and use its daytime hours for Cbeebies?