I've heard that having a core system is great for MMA, but I don't know if the core skillset is really that beneficial for fighters. The development of a well rounded game is what makes for champions. The "jack of all trades" development that lets them fight comfortably in different ranges where they have an edge over their opponent.
The current standout champions in each weightclass all have well rounded fight games and win their fights by exploiting their opponents weaknesses and bringing the game into another realm.
BJ Penn has good boxing skills with great submissions.
Georges St. Pierre has phenominal wrestling with really good striking.
Anderson Silva has good striking with a great ground game.
Fedor Emilenenko has great standup with phenominal submissions.
Even though he's not the champ anymore, Chuck Liddell had good striking, with incredible wrestling.
Forrest Griffin - good standup with a good ground game
Randy Coutore - good wrestling with good boxing.
For others a core skillset can be a hindrance to the development of their other skillsets
Maurice Smith - elite world class kickboxer, no ground game
Mark Coleman - olympic caliber wrestling, no submissions or standup
Kevin Randleman - carbon copy of coleman
Mark Kerr - carbon copy of coleman and randleman
Tom Erickson - carbon copy of coleman, kerr, randleman
Royce Gracie - elite level submission game, no wrestling ability and no striking
Matt Hughes - dominant grappler with elite weight cutting abilities (he was huge compared to his opponents), limited submission game and zero striking.
Kevin Jackson - Olympic Gold Medalist in wrestling, never bothered to learn submissions or striking.
Kenny Monday - same as jackson
Their expertise in each of their particular core styles lead them to rely on it instead of trying to fix their weaknesses by expanding their games. Some of them dominated competition for a while, then the competition developed more well rounded games and the old champions that were dominant in one thing fell as younger fighters learned how to negate their game and force the fight into a realm the older champs weren't comfortable with.
Even elite level skills aren't a gauranteed way to win. The current champs are good at everything, but most aren't world class in any individual area.