Those have a minimum thresholds. The Dutch company only has to charge destination country tax if their sales to Germany exceed 100000 EUR per year or 35000 EUR per year to France. And non-EU companies are not required to charge anything.

https://ec.europa.eu/taxation_customs/sites/taxation/files/r... column "Threshold for application of the special scheme for distance selling"

The UK import VAT has no minimum threshold, and unlike EU VAT the requirement applies to all countries.

The thresholds are going to disappear soon™

Yes, on July 1st, 2021, but they will be replaced with an unified threshold: If you exceed 10000 EUR in-EU cross-border sales in a year, you will have to charge destination country VAT. Otherwise you can continue charging seller country VAT.

Also, from that date, you will not need to register for VAT on the destination countries anymore, you can just remit VAT for all countries to your local tax office. Which is what they use as justification for lowering the threshold.

https://ec.europa.eu/taxation_customs/business/vat/modernisi...

I remember reading something about this, IIRC goods will join the VATMOSS scheme while the above thresholds apply before this happens (and the whole thing was postponed due to the pandemic). And VAT on digital services should get a threshold now

The VAT on digital services has had the 10000 EUR threshold since 2019-01-01. The same will apply to EU-to-EU cross-border goods starting 2021-07-01 when physical VAT OSS starts.

With the EU scheme the Dutch company doesn't have to register with the German or French tax offices. So while the Dutch company in your example would have to charge 19% VAT to its German customers and 20% to its French customers it only has to report and pay those taxes to the Dutch tax office.

So beyond the fee there is also an additional bureaucratic burden with this UK scheme.