I think it's hard to categorise songs as "perfect" or "wouldn't change a thing about it"... I mean, even in songs that I consider some of my absolute favourite I don't think it'd be too difficult to suggest small changes that might make me like it even more, or at least not impact how much I like it. At the same time, just because I think a song is "perfect" as in I don't think there's any small change that could improve it doesn't mean I necessarily think it's that good.
But just in terms of what band do I love that I rate even my least favourite stuff from them very highly, it'd probably be Alter Bridge. Even if there are songs I can easily pick out as my least favourites, in the grand scheme of things I still love those songs. They meet the at least 3 albums requirement - just. On a larger scale, I'd maybe say Mark Tremonti. Not including every song he's had a guest solo on or anything like that, as I don't even know all of them, but across Creed, Alter Bridge and Tremonti there isn't an album I can say I don't like (although I definitely don't rate the worst Creed stuff as highly as the weakest Alter Bridge songs).
If I were only including Labrie era stuff, Dream Theater would also be quite a contender as there are definitely no albums I don't think are great and no songs I can think of that I absolutely hate. But they do have plenty of stuff that's a bit weaker, and then taking into account WDADU, demos, B-sides and whatever I definitely can't say their weakest material holds up enough for me to say they've done no wrong.
Also, I'd say Seventh Wonder if I could restrict it to only their albums with Tommy Karevik. The songs from the first album are not necessarily bad but it just has such poor production and no where near as good a singer. But if I counted only the three after that they'd fit the bill perfectly.