Leaving the amp in between is actually a reasonable compromise. It is better to have nothing… no amp at center. Typically that would be mean running dual mono amps behind or adjacent behind the speakers. So, if you can’t afford monoblocks, then a centered stereo amp is preferred, because it is better to do the long interconnect run between preamp and amp than to have long speaker cables. Systems tend to be more favorable sounding with short speaker cables with a centered amp than with long speaker cables.
But overall… this is a pretty minor sonic difference in most folks systems. I have not done it in my current system. If I upgrade again, I will.