Tostado,
Not surprisingly, I've given that question a lot of thought over the years.
Here's my own take - in a (large) nutshell:
Peter Green and Jeremy Spencer - the two most blues-centric songwriters in the original FM - both quit the band pretty early on for mental health related reasons. That left only Danny Kirwan as a songwriter, and Kirwan has a quirky pop sensibility (evident on his solo records) in addition to blues inclinations. With Kirwan as the only remaining songwriter, it was likely that there would be a significant stylistic change in FM's music.
But, the band also needed a new instrumentalist to fill out their sound (just after Green's departure became inevitable). It's no real surprise that they turned to Christine (Perfect) McVie. Her band, Chicken Shack, was an FM sound-alike, they shared a label, and they toured together often. McVie had also already been a studio player on FM's albums, knew their songs, and had recently married John McVie before she signed on with FM. In retrospect, she seems like a pretty natural choice.
IMO, it was Christine McVie whose songwriting defined the future direction of FM. She's a blues player by trade (Chicken Shack), but a pop songwriter. On many of her songs (Don't Stop comes quickly to mind), there's a classic 1-4-5 blues progression (complete with turnaround), under the surface of the pop hit. You can hear a lot of the Buckingham/Nicks era FM in her contributions to the post-Green/pre-Buckingham/Nicks FM albums. At that point, having started the move towards a pop oriented sound behind Christine McVie's songs, they invited Bob Welch, another pop songwriter to join.
From there on, their evolution is pretty linear. IIRC, on the first, eponymous Buckingham/Nicks FM record, three of the first four singles (Warm Ways, Over My Head, and Say You Love Me) were McVie songs. Later, Rhiannon (Nicks) and Monday Morning (Buckingham) also got lots of radio play. Many years later, the Nicks tune Landslide became a hit. But, it was McVie's songs that initially drove the airplay.
I personally believe that Buckingham's ability to track McVie's songs to best effect is the primary reason the band became a radio success. Her songs were always there, waiting to be radio hits, they just needed to be polished and Buckingham is guy who (mostly) applied the polish. Then Nicks became a star for reasons IMO having as much to do with her personal charisma as with her music. When the personal drama of Rumours got the full voyeuristic attention of the record buying public, well - there you go, FM became king of the pop music world.
Ironically, tho I'll always love Peter Green's playing (and really like what Spencer and Kirwan do with a guitar, too), Buckingham has always commanded my interest at a higher level. He's the pop craftsman that can take a fair bit of credit for FM's sound, but his songs cover a huge range of styles, not all of which are radio friendly.
IMO, it's only when you see the band live, however, that you can appreciate the huge range of music that FM has mastered. The pop hits are there, of course, but you'll get experimental sounds on extended takes of songs like World Turning and/or Gold Dust Woman and/or Tusk, and monster electric guitar workouts like I'm So Afraid and/or Come. You may even get some old Green era blues rock, if Buckingham (along with Neal Heywood) fires up the absolutely smokin' version of Oh Well. And, as a bonus, Mick Fleetwood and John McVie are a monster rhythm section that rocks harder than you'd ever believe.
That's why FM is still my favorite live act, after all these years and all these stylistic and personnel changes.
YMMV.
