The biggest problem with having a shoutbox or chat system for support, is that there's no guaranteed way to search that. We only store so many shouts on a page, and even database table can get purged once in a while to save space.
When users look for support, the first thing we recommend for them to do is search. If users are looking for a way to get a FORUM button on their custom theme's menu on SMF 1.1.x, like the default theme has, then a search could lead them to the
General Custom Theme Tutorial. If they ask in the shoutbox and someone explains it, that's one more time that the tutorial has to be written out, and one more person's effort wasted. That topic's a sticky for a reason.
There are other topics, too, other issues. I've seen several people comment on others' support topics claiming they have the same issue. Sometimes those topics are months old, and their issues have been fixed by the solution in the topic. Sometimes they can help the developers figure out a bug by providing more feedback. But ultimately, the topics allow far more information and have a better retainment of that information for future users.
The last reason is, the entire Team is volunteer, nobody gets paid. So nobody's obligated to stay on SP.net watching a shoutbox to provide support for. Yet if we didn't, I'm sure there'd be complaints that the support shoutbox doesn't get attention, problems don't get solved, and we'd lose users because that would give us a bad name. While I love having competition to SP, as it keeps us challenged and motivated, I don't want to see people leaving SP for those competitors because we didn't provide what they needed.
Now, if we had the money, manpower and the community effort to do so, I suppose we could maintain a support shoutbox. It's much like many linux distros have IRC chatrooms specifically for support. Their community is large enough and motivated enough to provide support if they can, but sometimes they can't. There are forums for support as well for those groups, and I'm sure that their chat support is far less efficient than their forum support, mostly because of what I've talked about.
If you want to provide the money, the manpower (with the know-how) and the motivation, then it's probably something to seriously consider.