VAT and invoices are part of GDPR? Financial regulations yes - sure, of which the UK is pretty darn good upon.
But if a company invoices you with bad invoices then you can just refuse them and ask the correct and resubmit - even in the USA. As you say, you need them done right for tax reasons and believe me, countries and tax laws are tight, so to ask a company to redo it with the missing information is hardly going to be an issue - more so if they want paying.
The whole aspect of assurance of compliance you make though - very valid point. Just shame such things like GDPR need to be driven by countries and not some global standard that could be audited and approved that is not tied or limited by any country.
So if there was say some International standard with an ISO number outlining such standards, companies could adopt that and get certified compliant and it gets driven that way. As with many standards, adoption by insurance/reinsurance companies goes a long way indeed.