Yep! I totally understand EXACTLY what you're saying! Occasionally I will put on a record without checking for off-center and upon listening, I can clearly notice the problem. This is due to the center hole not being exactly centered (if you want to hear a perfect example of wow, use a junk turntable and junk 45, remove the 45 center, and purposely off-center the record, then place the stylus on the record and listen - this may be an extreme example, but it'll give you an idea). So what do I do about this problem?
(Short of trying to find a rare used Nakamichi turntable, which centers the off-centered record) What one can do is simply find where the groove "run out" is at it's extreme, then inconspicuously mark the label at that point, then carefully file that edge of the center hole until it rests against the spindle and allows the record to be centered. This takes trial and error but it's totally well worth the effort for the listening experience, no matter what. In my view, the record, no matter how valuable price-wise, is totally worthless if one can't actually listen to it just because of an off-centered hole.
Perhaps this is only one of several reasons (and I often say) CDs were immediately embraced by the "mainstream press and public" (if only they had real analog systems to listen to, then the industry would've been forced to refine the CD invention further before releasing it to the public market - unfortunately the industry brainwashed us that the 16bit 44.1k format was it! ....even then I asked myself, if CD was so "perfect" as they said, then why'd we need 8 times oversampling, etc etc? - but I guess I'm getting into another subject matter altogether so I'll end it here).
My thoughts.
......Paul