I am a UK citizen and have just also acquired Dutch citizenship. It seems that after Brexit on 31.12.20 that the EHIC services will probably no longer be available for UK citizens in Europe. I am intending to travel to Germany in January 2021. Would I be covered by the EHIC as a Dutch citizen? I have tried to research this and the wording I have found states that a Dutch citizen OR resident would be covered by the EHIC. However I am concerned that to qualify for EHIC as a Dutch citizen you would need a Dutch residential address and Dutch health insurance, which I do not have.
Your concern is well-founded. You need to be affiliated to the statutory healthcare system in another EU member state to be covered by the EHIC system. This means that citizenship as such is irrelevant, you really need to reside in the EU (even if you're not an EU citizen).
That also means that it will still be possible for British citizens to get a EHIC, provided they reside in the EU (whether under the transition regime from the withdrawal agreement or as a third-country national outside of EU law).