I don't quite see why a HL3 would necessarily be bad. Doom 2016 managed to be good despite shooters having changed a lot since Doom 1, 2.
What Valve really wants to avoid is a Doom 3 moment. When an old franchise is given a modern tuneup and the result is something nobody really thinks does the IP justice.
2016 was moderately successful. It got a lot of praise just for being stylistically Doom in every way that Doom 3 wasn't. But I don't think that Doom 2016 counts as strong evidence that HL3 could be made in a way that satisfies fans of the original games without alienating younger/modern gamers.