I worked on an ERP system for construction/architect firms in the 00s. The company was about 15 people when I joined, 40 when I left.
We consistently delivered migrations, but we hand crafted SQL extraction scripts, with data cleaning, etc. You could fully customize it, branding it with your own logos/colours/custom css, etc. There was just a clause that the "powered by" link had to stay visible.
I can't remember a single failed migration, though we were split into three "teams" each covering a different set of customers, so might have not seen one.
I suppose we were fairly small scale, and maybe those were the days where some serious attention to detail and care of the customer were still possible as generally we were replacing paper based workflows, not trying to migrate existing electronic workflows with huge data volumes.
But it's perfectly possible to do (and we worked with some fairly big companies in the space).
One of the funniest, yet saddest, support calls I remember getting was being asked "What do we do with Sue now, we don't have anything for her to do anymore?".
So it entirely depends on your implementation team I think. It's possible to do it well. But you probably need a very good set of consultants. If your ERP trainer is coming in and immediately setting up conflict with your company, that's definitely not a good sign.
Small scale is definitely another world entirely. My experience was not in the Billion dollar range as the parent, but in 20M+ (probably 50M in today's dollars) project territory.