In the game's current state, how worthwhile is it to pick up multiple core sets?

Very important as far as being competative, but if you don't play competatively I'd just print proxy cards of the ones you need in your decks. To get a full set (ie 3 copies of every card in the game) you have to spend about $200 extra.

Some of the best cards only come in one copy in the core set. Infiltrate, Pillage, Judgment of Verena, just to name a few. I'd look up a list of the cards in the set and decide if you want more of those one copy cards. The Core set can get you by pretty easily with all the three- and two- copy cards for friendly play, but competitive play might need more of those one-copy cards.