It doesn't even do that for most people in Ireland, according to its own map! As it appears to be based on land mass without regard to population density, the majority of the population would most naturally be in the Western European Time Zone, but they'd be pushed into the Azores Time Zone. A government in Dublin is not going to agree to a time zone change that wouldn't make sense for Dublin, and that's even ignoring the extreme political problems and potential violence and unrest involved with Ireland and Northern Ireland being in different time zones.

For that matter, Greece is understandably not going to agree to any change in time zones that results in a map where its islands that Turkey disputes are changed to be the same colour as Turkey, rather than Greece. Neither is Cyprus. It would be a bit like asking either the government of Taiwan to start using simplified characters, or the PRC to start using traditional characters, and simply saying that it would make language support on computers simpler.

I would support a reasonable proposal to end DST and have more natural time zones. But it has to at least consider factors other than just land masses and solar time, or it will never be a viable proposal. Their "full document" and "justification" doesn't include any discussion of the political ramifications or of population densities. They don't appear to give any justification of their specific country-level recommendations at all.