Not to defend them at all, but the longer it took to plan HL3, the longer it became a sounder business decision to just not do it for risk of not living up to the hype.
But Black Mesa is a counterexample; they still haven't released Xen last time I checked, but everything they have released far exceeds expectations. Maybe Valve should pay that group to finish the HL series.
Depends on how much you have to lose. Valve has a lot, and what they could win is a drop in the ocean next to "the steam tax". The icing on the cake is that there is value for them in competing less with those who publish on steam.
HL3 would have brought attention for sure but you are selling dota a bit short here. Personally I bought in day 1 to artifact based solely on how much I love dota. I have spent hundreds on dota cosmetics, battle passes, etc. Artifact failed because the game just was not fun to play at all. If the pricing scheme was the issue people still would pay money for a game they can't get enough of.
The longer they spent since last HL2 episode the more DNF the case became, and after few years it was certainly better to not make HL3 because it would fail horribly.