Was the ability to dock really worth taking out? I get it if the thing won't fit in the regular one, but surely it'd work with some 3rd party solutions.
You're assuming Nintendo's idea of 'handheld only', literally means it won't be capable of TV output. Remember, they also claimed the 3DS didn't support SDHC cards and the NES Joy-Cons were only for use with Nintendo Online's NES titles. I have a very strong suspicion the Lite will indeed be capable of outputing with 3rd party connectors, but only time will tell for sure.
Well, the reveal video stated plainly that the Switch Lite "Won't connect to a TV". Now, I don't know if they've physically removed the capability or not, but they didn't say something like "No dock support" or leave it at "Handheld only". But the "out of the box" could be implied I suppose. You're right that we'll just have to wait see; I'm just not betting on it.
Judging from past instances of what Nintendo claimed their products could and couldn't do, and by my understanding of how the hardware works (it shouldn't be something that can simply be left out, I believe they'd have to go out of their way to specifically block it), I'd say chances are very reasonable the capability will be there. I have a strong feeling that if I'm right, the built-in controls won't work when outputing-- meaning, you'll need separate Joy-Cons, which is why they'd rather not promote that feature.