There has never in the history of baseball been a time when a completely incompetent hitter could survive for long as a position player. The standard has always been that players must be at least competent at both.
Hitting is not everything, but a basic level of competence is necessary. A mediocre hitter will do fine if he can play excellent defense; Toronto’s Kevin Pillar is just such a player. He is a below average hitter but an outstanding glove man, so he plays every day.
Someone who literally was of no hitting value at all, though, could not possibly be a good enough fielder to make up for it. If a person hit like a pitcher, then unless they were a pitcher, it is literally the case that there are not enough baseballs hit towards that person’s position that are humanly possible to catch for their glove to make up for their bat.
To use the example of Mr. Pillar, he is not a **good **hitter at all, but he is competent. What I mean by that is that he is at least “replacement level” - while he’s not very good, he’s at least as good as some random guy you could get from an AAA team. Pillar does everything kind of poorly - he doesn’t get on base much, strikes out a fair amount, doesn’t have much power. He runs well but he’s not a superstar base stealer. But he is not SO bad that it kills the team. He has produced perhaps fifty runs for his team, where a regular center fielder would normally produce sixty or sixty-five by now. However, his glove is worth that difference (and more) so he’s a decent enough player. He is an exceptional defensive player who has saved perhaps 20 runs more than a center fielder normally would, which is remarkable.
Were Tim Tebow to be asked to play major league ball, he would not produce 50 runs. He would, if he was very lucky, produce perhaps 10-20; he is essentially completely inept as a hitter (Which is no insult; any 29-year-old who hasn’t played baseball in ten years will be inept.) Even if Tebow could play outstanding defence, which he can’t but let’s pretend he can, he can’t make up for it. If he was as good a fielder as Kevin Pillar he’d still be amazingly worse than the average Major League player; even if he were the best center fielder who ever lived, he STILL wouldn’t be average; the realistic limit on how much a center fielder can save you is probably about 40-45 runs. That would be* the best fielders who ever lived.*
Football is a poor analogy because a linebacker doesn’t have to play offense at all so his offensive prowess is irrelevant. In the case of basketball it’s actually not very common for purely defensive players to play regularly; a player has to have some offensive ability or he’ll be relegated to a bench role. But in baseball, a position player must be in the lineup. If you don’t want him hitting he can’t be in the lineup. You can use him as a late inning defensive sub but there’s a limited number of places on your team.
The only position where an incompetent hitter can play is pitcher, because a pitcher’s effect as a pitcher on the outcome of the game is colossal, more than an order of magnitude greater than any one fielder.
In effect, what I’m saying is that it’s the major leagues. You have to be at least moderately competent at everything or else you aren’t good enough.