jas After Brexit Day, whatever the deal, we would have no vote in the EU, even if we were to join EEA / EFTA
In practice, I expect the UK PM would be given the kind of input over decisions that the EFTA countries have, which is not via the EP, but mainly at heads of govt level.
Barnier is actually mainly trying to reassure May's Brexiter opponents by talking of this limited transition period.
So long as the UK is in transition, with everything working for the EU pretty much the same as now,
they don't mind if the UK spends 10 years there negotiating a good deal.
Trade deals usually take 7-15 years to negotiate - and that's when both sides know their own minds.
The EU is a past master at "stopping the clock" when it is in its interests
They have alway wanted a Norway++ deal (if Remain is not possible) and they hate No Deal
So, if the Uk / the negotiations need more time, it will be provided