Honestly, as people have said in other threads, Facebook is literally just a slower version if twitter, let alone the fact that people rarely use facebook for things else than communication between friends and family. Instagram is more for real life photos, let alone the fact that I've rarely seen a MC server use instagram to promote itself.

Social media sites like that are odd places to promote MC servers, and if used for that purpose, I'd deeply question their effectiveness of expanding the player base.

 

Instagram isn't really that good. Facebook is slow, as said above. Twitter is fast and reliable, thus why Twitter is used.

 

Facebook is slow. Especially on PC's (with my experiences anyway).

 

instagram gives you teenagers, facebook gives you middle-aged people. Twitter gives you anything between that. Twitter can be used for regular updates, it can be made so that each tweet posts on facebook, though.
But in general twitter is the most used platform. with ECC's demographic instagram and twitter would be better, but because of the nature of instagram (photos), twitter is left over.

And like you said, facebook, if used properly, can boost numbers.. for normal facebook pages. But that becomes a lot more difficult as a minecraft server. A minecraft server doesn't get as much engagement on facebook. People are more reserved about sharing anything game related.