Yes it seems "you need it to register your vehicle in the country you’re taking it to". Which is a joke really if you are travelling through various and many countries.

Aside from what you've already been told that under DVLA rules more than 12 months out of the UK classes as permanent export, basically what you say is correct. You could risk it and just ride home of course, but get stopped by the police, pinged on ANPR or have an accident and you're in serious trouble.

So the textbook answer is insure the bike online. You have no excuse not to do this anyway. Then google up the nearest bike shop to your port of re-entry, book an MoT for your arrival date and ride it straight there. You can then tax the bike online as soon as it passes the test.

On a more general note (and relating to the OP) it is usual that bikes need to be fully legal in their state of residence in order to be legally ridden abroad.

A little bit of trivia for you. In the UK vehicles (cars and motorbikes at least) over 40 years old are exempt from needing road tax and MOTs. This will mean that all you need is insurance and you are legal all over the world. No need to worry about getting caught owing off the ferry without an MOT or road tax.

Do any other countries operate such a system? If so can people register a vehicle there easily?

I think you will find that you sill have to tax over 40yr old vehicles, but it is free (zero duty), and apply for the V5 to be changed to histrionic vehicle status, and also proof that the vehicle is over 40years old to be able to be exempted from the mot.
In France there is no road tax anyway, and currently motorcycles do not need a control technique (mot), but you need proof of residency ( utility bill, copy of tax habitation), and a valid driving licence for whatever you are registering in your name.
Also any vehicle over 30 years old can be registered as a “vehicle collection” but the above criteria still apply.

Extract from the DVLA website

Bringing your vehicle back untaxed
If you bring your vehicle back to the UK untaxed you cannot drive it back into the UK - it’ll have to be transported and a SORN (Statutory Off Road Notification) must be made straight away.

And just to cheer u up further the Spanish police like to use the dvla site to check if u r legit . I speak from personal experience.......random stop check near port , its apparently due to ex pats using UK plated vehicles un taxed no mot etc etc according to the guarda chaps

I thought that was a pre Brexit thing as now we’ve ‘taken back control’ those foreigners no longer have access to our sovereign databases (:rofl:). No French camera speeding fines have caught up with me recently anyway.

I suppose there’s enough cops around in in France / Spain that someone has to get stopped by them but in my experience it’s pretty rare as a tourist keeping somewhere near the limits. In fact I’ve been struck by lightning more often in the 20 yrs than I’ve been stopped by the cops in either France or Spain. Is a loaded up bike really going to be mistaken for a tax dodging expat in a rusty VW?

It was a drink drive check IMHO but the officers commented on the bike being taxed .I asked the obvious question and was shown the dvla site on the officers phone . It was since brexit occurred . My friends campa was also subject to this when local police were checking car parks on the Costa del sol.....he was told ur tax is due in x number of weeks.......

Did he tell you when your MOT was due as well? Years ago I did get stopped by the cops on a bike (in London) for a ‘vehicle check’ I wasn’t speeding so he wanted to see if he could find some mechanical issue like no lights or non functioning brakes. After 15 mins or so of nothing he proceeded to warn me that my tax was running out in two weeks as though tax ran out gradually like tyres, so nearly run out was on the margins of an offence and I was lucky to get away with it. And they wonder why nobody trusts them.

They are also using this site to check insurance as well https://www.mib.org.uk/check-insurance-details/

I was stopped by a copper once who told me my tyres were almost illegal. I replied that was why I'd almost changed them.