Re: Unstable operation coming soon...
"I wonder whether the concept of a limited company will be allowed to continue under GDPR."
GDPR, exactly like the DPD before it, sets out a series of justifications for processing data. Put into context that means that publishing data is absolutely legal under GDPR as long as you can suitably justify it. In the case of something like companies house, the fact that the law requires the CH register to be public trumps the protections in GDPR. Even if it did not then there would be a strong legitimate interests argument.
ICANN have made no effort to come up with such a justification. Given that many registries already don't publish, that anyone can already register anonymously (for a fee, funnily enough) and the level of abuse of the public registries, such a justification is likely to simply not exist.