Well, that would be ideal. Sometimes it doesn't work.
Tony Oliva DH'd on one leg for three full years (1973-75) with the Twins. The general feeling was he had to hit a double in order to get to first base safely, which was only somewhat of an exaggeration. That seems ridiculous, but he did put up an OPS+ of 109 his first two years and 103 his third. Low for a DH, but perhaps better than anyone else the Twins had on the bench at the time. Bobby Darwin played RF with an OPS+ of 94 in 1973. Four guys played over 100 games in 1974 with a lower OPS+, including Harmon at 90. They pretty clearly didn't have healthy replacements better than Tony, so he DHd. Not ideal at all, but if you think the Pohlad payroll restrictions are nothing compared to the Calvin Griffith payroll restrictions.