No, there's no benefit for you to not select and download the games offered to you each month. PS Plus gets you a set number of games each month, decided by Sony--not adding these games to your library when available will offer you nothing except a missed game.
As to why the PS Network doesn't just automatically add those games to your library... they've never said why they don't, and I doubt they ever will, but there's a few obvious business benefits to Sony that they gain by not doing this:
Gauge Customer Interest: If 100% of your users get 100% percent of the games each month, you're limited in your ability to see what's popular. If 92% of your users add the RPG you're offering to their library, but only 80% of the users add the racing game you're offering, you now have valuable information about which genres are currently popular with your customer base, and you can potentially leverage that knowledge into more PS+ sales.
Better Traffic to Market: It's a well-known marketing tactic that just getting customers to walk inside your store increases sales, even if they don't intend to buy anything when they walk in. Forcing users to open the PSN store, where they'll be bombarded with ads for new and on-sale games, in order to get their free stuff, follows this marketing principle. (You can see people discussing this tactic working on them in the /r/PlaystationPlus thread here.)
Future Sales: If the game gets added to the library each month, and you forget to download a game you're interested in one month... well, no worries, you've got a copy in your library! The way it works currently, however, if you miss picking up your games then the PS Network--and the publishers of the games on offer--gets another chance at a future sale for every customer who forgets to download.
People May Not Want Them: It's worth noting that, sometimes, giving customers free things will upset them. See the U2 free iTunes album PR disaster for an example. People can have reasons to not want certain games in their library--imagine a religious person not wanting a game about evil gods, or a person with young children not wanting a violent game--and while of course the rational solution would then be 'don't sign up for a service that gives you free games', customers aren't always rational. Sony may benefit from heading similar PR disasters to Apple's off at the pass.
TL;DR the customer gains nothing from not claiming the free games. However, the businesses involved gain several benefits from keeping'not claiming the free games' an option.