You may be old enough to remember when the AL and NL were separate organizations. Each league had a president, its own umpires etc. Then it was decided to eliminate the league structures entirely. It’s now all just MLB. That the AL has the DH and the NL doesn’t is one last reminder of when the leagues were independent of each other. To me the DH is an abomination. But as you say, it is such a career extender, that players will never let go of it. Let the NL play real baseball and let its aging hitters drift over to the AL, just don’t ruin the NL by imposing the DH on it.
Here's an interesting point about the DH ... What other differences do the two leagues have in their rules?