Home Run Derby helps make the case for pitching neutral games, i.e., use a pitching machine.

Home Run Derby is popular because the pitcher is neutered.

http://m.mlb.com/news/article/188521894/2016-home-run-derby-field-is-set/

Players were seeded one through eight, based on home run totals through Wednesday. As the top seed, Trumbo will take on No. 8 Seager in the first round, with the winner of that head-to-head battle facing the winner of No. 4 Cano and No. 5 Stanton in the semifinals..

On the other side of the bracket, No. 3 seed Duvall faces No. 6 Myers and No. 2 Frazier meets No. 7 Gonzalez in the first round

The winners of those two dinger duels will meet in the other semifinal. Then the last two sluggers standing hack for the hardware in the final round.
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What, you thought there would be a neat list. It was difficult enough to find this. And who writes that stuff? More rules follow but there is no mention of the pitchers. Based on previous years of this horrendous event, someone will stand behind the batting practice screen for protection and will lob meatballs to home plate from a distance much shorter than that in a game.

In other words, it's like a pitching machine that throws really slowly. No wonder there was some talk that a pitcher might participate. Pitchers do not hit well by major league standards but that's against their peers. Against meatball lobs, anyone can tee off. Madison Bumgarner was the pitcher suggested as a participant. His ERA+ is 206 and yesterday Bumgarner pitched nine innings: 1 hit, 1 BB, 14, SO; 4-0 shutout. Oh, batting Bumgarner was 0 for 4 with 3 SO.

Bumgarner has 13 career home runs in 417 at bats. OPS+:
career 47
2016 52

In other words, he sucks. But he's got 5 HR in 50 AB in 2016, so some idiots think that he can hit ... well. He cannot. If he could, he would ... be a baseball player, not a pitcher.

But here's the thing: remove pitching and you've got an entertaining game, not this ritualistic, ceremonial bore. Players will hit, field, and run the bases. No pitching of any consequence. Even Bumgarner could play. And the other pitchers, assuming that they have some hand eye coordination. And they won't become injured at any movement that's not predefined and practiced repeatedly ad nauseam.

Tee ball would work but if you want batters to be more challenged, and probably eliminate "pitchers" from becoming players, use pitching machines.

Both teams would face the same "pitching". If you want to spice it up, have the machine mix in breaking pitches. But have the degree of difficulty be the same for both teams. That would make it a true competition between teams of baseball players.