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Are you shooting full frame or crop?
If you're shooting crop, 70-200 should be adequate for youth baseball. I've found that 300mm is too long for most shots on the youth baseball fields around here, at least on a crop body.
The majority of my high school baseball work occurs between 110-170mm on the local high school field.
You really only need 300+ for the higher levels of baseball where you can't get as close to the field, IME.
YMMV.
I found a 70-200 on a FF, with a 1.4X works out quite well for baseball. For baseball you really don't need a F/2.8 for isolation. Typically, there is enough open field behind the action to minimize a distracting background, without the need of a wide aperture DOF.