Question Author
NJ you make a fair point, but I think you are conflating two issues: one is having documentation that you have had the two vaccinations and the second, how that documentation is put to use.
As an aside; having a booklet which contains all the vaccinations and dates when the person has had them, is considered an asset to both the holder and the medical profession, not an imposition, in some countries - as I've outlined above.
And, can you actually envisage hired 'bouncers' standing at the doors of busy pubs & restaurants checking documents ? I don't think so.
A one-off certificate of covid vaccinations would only be used & be of use while this odious epidemic lasts. Someone above has suggested a stamp in a passport which would be an excellent idea, & before someone comes forward with the usual 'not everyone has a passport' argument, well there are simple alternatives to that for them.