It wouldn't be impossible for Danish manufacturers to produce CEE 7/5 (French) or CEE 7/4 that were compatible with Danish boxes for retrofitting purposes. I guess the recess would be perhaps an issue if they're shallow, in comparison to a flush-flat socket, but there are French designs with relatively shallow boxes too.
Italy's seemingly moving to Schuko by gradual osmosis. The Italian standard seems to be still there, but there were loads of buildings with Schuko sockets installed that weren't hybrid types. From what I gather too most appliances seem to ship with CEE 7 plugs.
I'd nearly prefer the French approach - at least there's a possibility of polarising it and the current generation of socket outlets seem to incorporate mandatory shuttering. There's also a flat version that has a push-in front. https://www.legrand.fr/catalogue/prise/prise-de-courant-avec-terre-celiane-surface-avec-plaque-blanc
They also seem to be made as a single unit, even if they've clip on facia plates. The design is a lot more like BS1363. Schuko outlets seem to be quite different with the removable front plate that exposes the innards of the socket.
It's going to be interesting to see how Ireland deals with post-Brexit EU as the supply chains will quite likely change towards continental ones, which will result in a lot of appliances arriving with Schuko and CEE 7/X plugs again.
We used to use Schuko decades ago, you'd certainly see plenty of it in the 1960s. However, we standardised on BS1363, which is IS401 plug (IS411 socket) here.
At present there's no real discussion going on about it but, I would assume that if it became problematic we might ultimately shift back.
There are a couple of scenarios where it could become problematic:
1) The UK drifts away from CE and European harmonised electrical standards for appliances. That could result in appliances manufactured for the UK market becoming unmarketable in Ireland. So, we would have to shift to continental supply chains.
2) The BS1363 standard itself could end up incompatible with harmonised European standards, although frankly that's extremely unlikely. The current plan is that we will just maintain it as IS401 / and IS 411 and would get approvals for it via the NSAI here.
I can't really see a situation where the UK wanders off into lax standards, and I would assume that most International manufacturers are likely to continue as normal. The only situations that could perhaps arise is if the UK were to say start accepting some future Chinese standards or harmonising with Australia and NZ and so on.
However most of these things are ultimately coordinated by bodies like the IEC and CENELEC is not an exclusively EU body, although its standards are compulsory within the EU, there are other members e.g. Turkey, Switzerland etc. Even the likes of the USA are associate/observer members.
It'll be interesting to see what happens though!
My personal preference in Ireland would be that if we did switch, it would be to the French CEE 7/5 system - possibility of keeping it polarised and also the contemporary French / Belgian sockets contain mandatory shutters which would keep continuity with standards we've had since the introduction of BS1363.
However, from an ease of standardisation the CEE 7/4 Schuko socket outlets might be more of an open standard and I assume would could still mandate shutters on those.