Virtual shelves? Free dollars? Yuck....
The idea I would like to see on GOG.com: an option to get a physical CD/DVD copy (not burned but "pressed", industry-standard disks) of a collection of games I purchased, with a nice cover and a DVD-style box to ship to my home.
That would be fantastic....

While I totally agree with the rest of your post, I can't agree with that sentence. As GoG is, by essence, selling a dematerialized product, providing a customer with an already available game costs almost nothing. They have already negotiated and fixed the game, the only remaining cost would be bandwidth, that is almost nothing.
However, if they give you a game that you were going to purchase, they would actually miss an opportunity. Maybe this whole virtual money thing could work, but only if you cannot choose the game you'll get : when you have enough GoG$, you are rewarded with a random game that you don't already own. They might even excluded the top-ten most bought games, for instance. This way, the probability that they offer you a game you were going to purchase is very low. And you get a free game that you wouldn't have experienced otherwise, and which might be a good surprise for you. And if not, well, you haven't lost anything, Gog either, and Gog is still awesome.

That's essentially what I meant, that is, people would end up getting for free the games they otherwise would have paid for outright. A rewards system that allows people to save up points for games, regardless of what games they are, could end up costing GOG some sales and in that sense, losing money.

No reward system.

Fine, then ;-)

Sounds like a good idea, elsewhere thou. Gog is already as cheap as it can get and to be honest, getting "free" games would feel like stealing.
Good idea, wrong time and place.