No reason to eat it, like, ever? Or just today on June 4, 2024? Because I agree with that latter, if for no other reason then we have no one in-house whom we know is better.
As for value on defense and baserunning, yes, he probably has positive value on both, but sometimes that's not enough to overcome truly execrable hitting, and all parts of the game are additive in terms of what it means to wins.
The problem is, Javy may not have as much of either going for him as we think. B-R has him at 0.2 dWAR so far this year, and Fangraphs actually has him as a -0.1, with minus-1 defensive runs saved and minus-2 outs above average, mostly because of his throwing woes, but also, the ball is clanking off his glove too much. I know FPCT is a discredited statistic, but he is no better than middle of the pack in it, for what that's worth. I understand it's hard to believe Javy even might be a minus defender, because he makes such visually spectacular plays, but remember how Derek Jeter compiled a historic highlight reel of appealing defensive plays, and he was still one of the worst everyday defenders at shortstop in the game.
As for baserunning, again, take this for what it's worth, but Fangraphs has Javy at 55th of 155 qualifiers in XBR, which is Statcast baserunning above average, putting him behind Riley Greene, Matt Vierling—and Mark Canha, believe it nor not. Javy is above the fold, yes, but not by as much as we might imagine he would be.
Add it all up, and if we had a better alternative ready to go, I would conclude that Javy Baez's defense and baserunning would not be enough to keep him employed here for much longer.