This is a co op. I can see this argument for the competitive LCGs, but for this game it's pretty weak. You can just proxy or borrow cards from your friends if you feel like it's that big a deal. If you are playing with just your collection then everyone has the same handicap and the difficulty is completely adjustable.
First off, I have a personal distaste for proxy. If you are willing to proxy any cards, you are willing to proxy all cards, and so why are we talking about money in the first place. The value of any of the cards is not the "idea" of the card, the idea is given practically for free online. It is for the execution. The thickness of the cardboard, the art licensed and the design work implemented. For those who look at proxy as a valid way of overcoming an incomplete collection in a deckbuilder, we will just always have a difference of opinion.
Sure, this is a co-op game, but that both supports and distorts these arguments.
Borrowing cards from your friends works how? Short of completely merging the collections (at which point you paid for two cores, and then split the cost) you will always have to dedicate some amount of time in each game session to separating the collections. It is trading time for money, and some people don't want to spend the time. let alone the idea that you are now limiting yourself to only play with your friends. Playing this game with aquaintences or strangers can be a great experience and can lead into more freindships...but do you really want to start that relationship by saying "oh can I go through your collection and borrow these powerful cards for my character for today?"
The scenario where you only use your incomplete collection and that you just acknowledge the handicap and only use the "easy" modes of the scenario's drastically reduces the value of the game as presented. We all play these games to hone skills and get better at the games we play. We can't get better without increasing the challenge. And lets not also forget that idea that we may play with others who are used to playing the hard mode, but when they play with us, they have to play on easy because we haven't spent money on cardboard just to throw it away.
Again this is based on the idea that certain deck types and strategies based in the core sets are expanded upon in the expansions. If a new deck type is developed in the expansions, then sure, the expansions alone can help you to create the resources you need to tackle the harder difficulty scenarios. But if you keep building decks through the life of the LCG thinking "ugh if only i had 3 copies of X card like everything else, this deck would come together" then you have a problem.