This is something thats been debated several times just in my 3+ years on this forum. Have a look at some of the old threads and you'll get some good arguments on both sides of the debate.
The truth is that we don't know if NIFCs will increase in value over time. I say no, or at least not soon enough to make it worthwhile. I look at the 1987 half as an example. It was NIFC just like the 2002-2013 are. That coin is now 26 years old, and there is still no real demand out there for it. Sure, you occasionally hear about someone selling one for a profit or a coin shop that pays a small premium for them, but these instances are pretty rare. I've seen many more instances of people saying that their coin shop didn't want their NIFC halves and/or they were unable to sell them for a profit.
Value comes straight from supply and demand. The mintages (supply) are indeed low (not SUPER low, but pretty dang low) for the NIFCs. But right now, so is demand. Could that change? Absolutely! But I'm betting that if NIFCs become "worth keeping", its so far down the road (50 years+) that there are better things I can do with my cash in the meantime. Had I kept all I've found (and I'm not a high volume hunter), I'd have well over $1000 tied up in these things. For such a low mintage, there sure seem to be a bunch of them floating around out there. Also, I believe that if this "down the road" scenario does happen, collectors will want MS-65+ NIFCs as these coins were only issued in mint sets and collector rolls if I'm not mistaken. The "impaired" examples that we generally find likely won't cut it IMO.
Bottom line is that if you like them and/or think they'll increase in value in the future, by all means keep them. Its your money and your collection. Do it your way!