Do it. Just do it already.
Make all of the hypothetical arguments you want, but not having the designated hitter in the NL at this point is a terrible argument. The DH does several things: provide an optimal offensive line-up and give aging sluggers with no defensive value a place to continue hitting. It also saves pitchers from embarrassing themselves, waving the bat like a T-baller. No more automatic outs unless you have Carlos Mendoza in the line-up.
It’s the reason for the disparity between the NL and AL.
Keeping the DH in one league and not installing it in another is Draconian at best. Installing the DH league-wide is logical.