That's easier said than done in a cap system.
UFAs are players too and need to get paid also. They have a longer proven track record than their RFA counterparts to justify the premium in their salaries. UFAs are part of the collective PA, so it's not as if they could simply be pushed aside in favour of RFAs. An argument can be made that the max term for a UFA should not be longer than 5 years (so as to avoid having to pay for the less productive years after they turn 32 to 33), but that will simply push up their AAV, which will have an adverse effect on the cap. You can theoretically force players out of the league in their early to mid 30's by overpaying RFAs because there's only so much money to go around in a cap system (that already happens organically as older players in their mid to late 30's retire, and those who play beyond 40 are just rare breeds), though why will anyone do that in a unionized labour workplace?
The problem with paying RFAs huge sums of money is most of them have only been in the league playing consistently for 2 to 3 years, so their sample size for their production is relatively small compared to UFAs - you're betting mostly on potential rather than consistent, tangible output through a longer period of time. This is risky in two folds: first, if they justify their perceived over payment, then they can be overpaid significantly when they reach UFA status; secondly, if they don't live up to the value of their contracts, you've tied up your cap with bad contracts for significant time, which weakens any team's position to support the roster (and that includes being able to sign over-priced UFAs).
UFA salaries won't come down (especially at 27 to 28 years old) even if RFAs are paid alot more, and that's a major problem in a cap system. If anything, this will destabilize teams even further...maybe that makes it more exciting for the league and for player movement, but it will definitely be more stressful for everyone...we already witness these dynamics in play where teams scramble to trade away young assets that they can't afford to pay, trade potential UFAs for younger and controllable assets, or simply let them walk.
The key to stable, reasonable RFA salaries is in the negotiations between the owners/management and the players and their agents. It doesn't take much for an imprudent owner/GM to destabilize their own salary cap structure by overpaying RFAs at their own peril.