If it was possible, somebody somewhere would be doing it, be it Mechanicus or Inquisition. I can't really see the =][= not churning out an endless stream of GKs if they could do so.
I've never read anything that stated that. I think the instability had more to do with the fact that it was often attempted on people beyond the ideal adolescent age group for the process. All the primarchs had a bunch of grown-up comrades, retinues and sidekicks that wanted to join them on the crusade and were willing to put themselves through such a dangerous process to achieve that. Not all of them were successful.
The Horus Heresy had also revealed weaknesses in the gene-seed of several Space Marine Legions. These defects had been exacerbated by the accelerated gene-seed cultivation techniques needed to keep the huge Space Marine Legions up to strength. Guilliman believed that the Chaos powers were able to exploit the resultant physical and mental corruption to turn Horus' troops against the Emperor. One of the key objectives of the new Codex Astartes was to recognise and expunge these genetic weaknesses. As a result, the Codex Astartes decreed that Space Marines would forever more be created and trained slowly. The genetic banks used to create Astartes implants would be carefully monitored and scrutinised for any defects. Cultivated organs would be subject to the most stringent tests of purity. Young Initiates would undergo trials of suitability before they were accepted, and only those of the very sternest character would be chosen.