What's so bad about cover albums?
Tsunku covered A Hard Day's Night. (more for his own vanity though)
W's first was a cover album.
The entire Folk Songs series were covers.
Cover You is damned good.
H!P appearances on Music Fair 21 and Uta Doki were also great showcases of H!P and covers.
I get conceptually why cover albums may be objectionable, as some people fetishize originality for originality's sake. But if you've they're good songs and you're not familiar with the originals, they might as well be new songs for all you know. Why does that deserve more spite than say, the current Morning Musume singing Morning Musume songs from over a couple years ago? Those are essentially covers too, right?
But yeah, ever since about 2005, I'd say Tsunku has been writing fewer songs for H!P. Basically he was only writing for Morning Musume, V-U-den, Berryz, C-ute, and Gocchin. Everyone else was singing songs written by other songwriters. Don't forget that Tsunku is the executive director of TNX, has his own restaurant, produces health socks, has a wife and twins, now has his foot in the door of the video game industry with Rhythm Tengoku, and still manages to find time to write songs and produce idol acts. The guy has a lot more on his plate now than when he wrote almost every song for every H!P act. I have nothing but respect for the amount of work Tsunku takes on.
Back to the issue at hand, a 4-member group from a few years ago, eh? Since a new Minimoni is in the works, we can probably rule that out. T&C songs are generally a little more technically demanding and mature sounding than a group as young as S/Mileage can do, but C-ute covered some of their songs, so it's not completely ridiculous. 4-nin Tanpopo songs seem about right in tone for a younger group, but somehow it just doesn't seem to fit. Unless we're talking about one of these groups, or maybe Coconuts Musume *snicker*, we might have to look outside of Hello! Project for a 4-member group.