I'm like that, and it might not be a majority way to listen, but it's not uncommon at all either.

Importantly, I think you get A LOT out of your music/artist that way.
(Disclaimer: Different strokes for different folks and all that. . . )

I have several friends who buy/download entire discographies (sometimes even of swaths of a genre), and they simply don't get around to listening to a lot of it, they often miss out on actually appreciating an *album*, and they simply don't get as "into" a band as listener's like you and I. Which is fine, but it truly is experiencing and imo appreciating the music less.
With all my favorite bands, I know virtually every song on every album. And I do like LOTS of bands, so I really don't feel limited at all. But the best part is the love, appreciating, and connection you make with a band (or person) that you truly know. In many ways I feel like it's similar to having 100 friends versus having 5 really good, close friends. I think we all know which type of person truly knows and appreciates their friends more. . .