The Beatles is a proper name because it is unique to that particular band, just like The Rolling Stones, and The Bee Gees . But "evergreen trees" is not a unique horticultural name any more than "deciduous shrubs" or "bedding plants" is. "Trees", "shrubs" and "plants" are just common nouns with a modifying adjective or another common noun plonked in front of them.
In writing, you can call Ringo Starr a "Beatle", Mick Jagger a "Stone" and Barry Gibb a "Bee Gee" since they were each a member of a group whose name was proper name. But if you wrote Mick Jagger was a "stone" (no capital) that would have a different meaning, and if you wrote that Ringo Starr was a "beatle", that might imply that he was a creepy-crawly! It simply makes no sense not to capitalise "Beatle", "Stone" and "Bee Gee".
Of course, it only works for members of groups with a plural proper name. You can’t say, for instance, that Roger Daltrey was a "Who" or that Freddie Mercury was a "Queen" (or maybe you could!!!).