Ya there's plenty of reason to do it, it is just clear Valve has lost interest. They seem to suffer from "Oooo shiny!" syndrome pretty bad, which they can afford to do since Steam makes them more money than they know what to do with. They'll play with a project for awhile, get bored, and move on to something else.
I mean I can respect not making a sequel just for a sequel's sake. If the series has run its course, it sucks to tell the creative people "You have to make another one, no I don't give a shit how much it doesn't fit!" Clearly not the case here, they had more story to tell so the creative types should be happy to continue it.
Likewise I can understand not making a sequel if it is going to be a commercial failure. No matter how much you'd like to continue something, if the market isn't interested it is a bad idea to do. Again, not the case here, the game could be crap and it would still make money because so many people want it bad (not that it matters because of Steam).
So there's no reason not to do it here, only that Valve is flighty and isn't interested in it anymore for whatever reason. I mean all the crap about innovation is bullshit. Valve is happy to do things that are just more of the same. See Left 4 Dead 2, DOTA 2, and CS:GO. Left 4 Dead 2 was really just an expansion pack sold as a new game, DOTA 2 is just a MOBA, one of a shit ton of them and one that borrows heavily from others, and CS:GO is, well, Counterstrike. No problem, I'm not hating, but trying to claim that they somehow have to be really innovative with their games is crap. They have been happy to release games lately that are just rehashes of existing stuff.
I guarantee if the Steam money pit dried up they'd be looking to make HL3 really fast. However they don't have to care right now, they can just play around since they make shit tons of money for doing nothing but being a middleman.
It also shows lack of commitment to their projects, specifically the Steam Machine. Valve really is half-assing it (as is obvious from the timeline, that there is on QA on the various platforms, and so on) if they really wanted to try and drive it, HL3 would be there and be used. Make that a Steam Machine/SteamOS exclusive people would give a shit. Even if it was just short term, and then it comes to Windows, it would massively push sales having an exclusive title that people really, really want. Existing console makers know this, and always try to have a killer franchise. Were Valve really committed to their new toy, they'd have HL3 ready to go for it.