Would changing the Designated Hitter Rule from starting pitcher to any player help Shohei Ohtani?

Here's the rule Designated Hitter (DH) rule from http://mlb.mlb.com/documents/0/8/0/268272080/2018_Official_Baseball_Rules.pdf:

5.11 Designated Hitter Rule

Any League may elect to use Rule 5.11(a), which shall be called the Designated Hitter Rule.

(a) The Designated Hitter Rule provides as follows:

(1) A hitter may be designated to bat for the starting pitcher and all subsequent pitchers ...
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There's plenty more junk as you might expect but the point is that the rule always made even less sense than the obvious: it should have been a designated fielder rule. Whatever you want to call it, it should never have been restricted to the pitcher. Even way back when it first started in the old American League in 1973 it obviously did nor allow for a Babe Ruth, someone who could excel at both pitching and hitting.

How much did Babe Ruth pitch and bat at the same time? Monday, April 9, 2018

Babe Ruth batting order position when pitching. Tuesday, April 10, 2018

This seemed irrelevant until 2018 when Shohei Ohtani came to the U.S. from Japan to attempt to excel at both pitching and hitting, i.e., to be another Babe Ruth. So far Ohtani has succeeded. His team the Angels could petition to have the unnecessary restriction removed so that in 2019 Ohtani can bat when he is the starting pitcher in American Conference parks without his team losing the DH.

But here's the problem. The Angels would be faced with having relief pitchers coming to the plate after Ohtani has been removed. When Ruth played complete games by the starting pitcher were common. In 1917, his last season as a full time pitcher, Ruth led the American League with 35 complete games. So far in 2018 the Angels have played 26 games and the starting pitchers have completed none. The starters, including Ohtani, are averaging no more than five innings per start.

Would the Angels be willing to deal with having relief pitchers bat to get Ohtani's bat into the lineup even for only three plate appearances? It's not simply the same as not using the optional DH because it would be replacing their weakest hitter with a better hitter, along with Ohtani batting for part of the game.

Let's say that the Angels designate the catcher as their designated fielder. Here's the likely result:
- Ohtani bats three times but then pitchers or pinch hitters (PH) bat
- the DH bats instead of the catcher.

The Angels would essentially be swapping 1 or 2 PH situations for removing 4 PA by their weakest hitter AND ... have Ohtani bat three times.

Last night Ohtani belted his fourth home run off Yankee starting pitcher Luis Severino. Ohtani now has 4 homers in 44 at bats. That's one every 11 AB. If Ohtani somehow managed 500 AB and homered at that rate he'd hit about 45 home runs. So, yeah, I think the Angels would want that option.