You get them whether you want it or not, at least some of the time. Entropy and so forth. The synthetic ones with worse imperfections are cheaper.
It's probably possible to guess by inspection whether the imperfection properties imply mined vs lab grown, with some level of accuracy.
Source for the existence of imperfections is reading through lists of specific diamonds a few years ago. The synthetic ones didn't vary much in colour but did vary in number and distribution of inclusions.
This is Gary: his job is to give the machine a solid kick once a day and crack the vacuum seal on Fridays. Gary made us 120 million in imperfections last quarter.
Why can’t you add impurities when manufacturing a diamond? “Doping”