If by a couple of months you mean more than 6-9 then yes. Darksiders 2 has been out 6 months and it is still $50. That game has never been lower than $30 plus it has a season pass. It did not even sell that well either. So with a new system you are looking at $20 games most likely summer of 2014 at best.
It also assumes that with no used market that games will drop at the same rate which may not happen without competition.
This is true. I've bought Batman Arkham City GOTY and Saints Row The Third on PC each for under $7 I think it was. Sleeping Dogs has been $10 for PC. Darksiders 2 has been as low as $9. Hitman Absolution $17. I've already bought the upcoming Tomb Raider (don't laugh) for $33. The games are just always cheaper for PC compared to console. They also look better and I just grab my laptop, connect it to my TV via HDMI, and use an Xbox controller and I've got better games for less money (not counting the cost of the PC/console to begin with).
If Sony and MS were to both go the no used games route they're going to have to compete with price or people will just game on PC/Steambox and get better graphics and prices.
I'm still going to be in shock if one company (MS/Sony) does this but the other doesn't. I just can't really believe either could possibly be that stupid.