pcr amplifies all sequences, correct or wrong, no? and as I understand it, it works on short snippets the best.

It amplifies sequences that contain the two primer sequences on each end of the target. So if you had synthesized sequence XYZ with some mistakes like YZX, then you could target X and Z and purify.

You're correct that PCR has a limited max length, but it is longer and cheaper than vanilla DNA synthesis.