Music is like a tapestry, made up of many threads, all of which can play a part in enriching the overall picture.
Guitar work is undoubtedly more prominent in some of the branches of the Alternative scene - for example, singer-songwriters in an intimate setting, or roadhouse singers, will very often make a guitar a key feature of their performance. But when I think of women who are truly outstanding instrumentalists, it tends to be particularly Bluegrass and the Blues that provide that opportunity to shine.
(For instance - here's a Blues performance from a female artist who really is in a league of her own. I don't think anyone could seriously say here that the guitar is being used as a prop, or a safety mechanism - or that the instrument is distracting or getting in the way of her vocal - the genre expects this interplay of both elements to express that level of emotion)
https://www.youtube.com/watch?v=XT4Lr_oVGQY
However, in Mainstream Country, the tradition of singing, and the audience expectation, lead to a different emphasis. There's a well known saying, from Harlan Howard, that all you need is 'three chords and the truth' - and while that was always an exaggeration, with the Nashville Sound never fully managing to drive out the traditions of Country Rock & Roll, it has often seemed fairly close to the impression given by many of the lead singers.
If you think of the place Carrie inherited in her own dominant career, women she covered on her independent albums (e.g Patty Loveless), was compared to at the Opry (Connie Smith, Barbara Mandrell), or was widely seen as emulating in her vocals (Reba McEntire, Martina McBride) they were often ones who seldom played a guitar in their best remembered performances
(Of the women who perhaps most influenced Carrie, Dolly Parton may be the main exception - she often accompanies herself on guitar - fingernails notwithstanding! But Dolly's Mountain tradition, and. early start, touring with her uncle Bill Owens, was rather different. Miranda Lambert also could be said to have had different beginnings, falling asleep on her father's lap while he was strumming acoustic guitar, and undertaking her own early tours with just one accompanist. Also, Miranda has always remained temprementally closer to the Country Rock tradition exemplified by people like Waylon Jennings and Merle Haggard, while the women she mentions are often Blues singers.)
So I think it is fair to say that Carrie's main performance tradition has been that of the concert stage vocalist - which tends to place much less emphasis on an instrumental role for the lead singer. That said, though, I think there is ample evidence that she is interested in instrumentation. The cover art for her second independent album had a shot of her with an electric guitar, and there is early footage of her performing with acoustic guitar. She has been seen carrying a guitar case to writing sessions. She also plays piano, and in recent years has experimented with mouth organ, percussion, and (I think) saxophone. I'd also make the point that her concert performances of Smoke Break, for example, show real joy and enthusiasm when she faces off with other players, or finishes with solo flourishes. I'm certainly one who admires Carrie for many reasons - not necessarily primarily as an outstanding singer (her loyalty to and understanding of the long run of tradition in Country Music being not the least of those reasons for me.) As it has tended to figure strongly in my musical appreciation over the years, I would welcome more playing of her guitar on occasion - even though I don't expect it ever to be the man element in her very successful performance career.