I don't mean to rain on your parade but here are some problems I find with your list. (The numbers will represent the # on the list I am referring to.)
1. True, Carrie does have more #1 hits but that's on the country charts where #1 hits are easier than on pop. Plus, Carrie has one number-one hit on the Billboard 100 chart and I wouldn't really call it a huge, signature song unlike the other artists' that you mentioned #1 hits. Glee usually likes to put well-known songs into their episodes.
2. Justin Bieber and Lady Gaga have only been around for a little over a year so it's unfair. Carrie isn't in her "pop" peak anymore (aka Some Hearts era) unlike these two artists. So Carrie won't attract as big of an audience as other artists. These two artists are also pop stars so they're more likely to have fans and just random curious people who are more eager to turn on Glee than country fans.
3. I don't watch Glee so I can be so sure whether or not they feature many religious songs. Carrie has hardly released any love songs as singles. I did hear Glee was having an alcohol-themed episode so maybe wasted could've fit that but with artists like Kesha and Jamie Foxx, her country-er songs will feel out of place in most episodes.
4. A celebrity hellish decent is what makes the artist more intriguing
5. BHC is a specific song so if they sing this, it may seem like they're stealing a plot from the song. (I mean the guy cheating then busting of car, not all the verses. And singing this during the episode will make it seem more stolen.)
7. I'm not sure if your implying Carrie be on the show or not.
8. I think a country episode is being/has been filmed.
9. I think it might turn some Glee fans away because a lot of pop fans HATE country music. The not-as-obsessed Glee fans might not watch.
It would be a great boost in her sales and I probably would watch an episode featuring Carrie. Not many artists are featured on Glee so it's already an honor to be featured. Other than Lady Gaga and Rihanna (excluding special episodes), not many artists, even really successful ones, are featured more than twice on Glee. ex (with one Glee-covered song): Beyonce, Kesha, Kelly Clarkson, Jordin Sparks, Katy Perry, Jay-Z, etc.
