The rule does make a one-dimensional player more comfortable, and more valuable.
No doubt there.
Of course, it does not have to mean teams go get those players.
A well-rounded team can pass the DH around, and there's an advantage in that.
And if a pitcher is well-rounded enough, a team can DH for another player, though that would be quite rare, and probably rather embarrassing for that player.
Two leagues playing for the same prize using such a different rule always bothered me, more than anything else.
Either get rid of it entirely or make it universal.