Cutting him gives up a zero cost option for no reason.
I totally agree with you that's how it "should" play out, but Bradford's agent is a master of maintaining contract leverage and cashing in on that leverage, and with the Rams it's that value of the lost opportunity of simply cutting him (the "zero cost option for no reason" as you put it.) that will get all the air play. From the start Bradford's agent will make it clear he will not sign any new contract -- let alone a bonus-only deal -- and there will be stories leaked about what a shame it will be if the Rams just cut him and get nothing for their millions of dollars invested after so much bad luck (and now that he's "fully healthy and looking great in his workouts!").
So I think the counter-intuitive result is more likely -- if the Rams want to keep him, it might actually force the Rams to just keep him at the same contract for the final year. If there is any contract relief from Bradford's agent, it certainly would not be bonus only, there will be a price for that help -- some amount of base, maybe even small guarantee included. Otherwise, his agent will say "the Rams aren't living up to the final year of the contract despite that SB is healthy and ready to go", just walk and sign with another team.
Your scenario is awesome from the Rams viewpoint since a bonus-laden deal gets his cap figure down towards the $4mil minimum hit, but for those that want SB back, I don't think it should include the high hopes that keeping Bradford will also include big cap savings -- his agent just won't allow it. In the unlikely case SB overrules his agent and wants to help, it will be small help. I wouldn't count on keeping SB for anything less than $10mil to the cap and even that's a pipe dream, most likely it will simply cost the current $16,580mil cap hit for one more year of SB in 2015.
Sadly, it's the worst reality -- instead of a home town discount, his cap hit to stay with the Rams will be more than if he just was cut and signs with another team that doesn't have to worry about the baggage.
This is the same situation that we had with Wells this year, (anyone still unhappy that we didn't just cut him?).
Yes. I am still unhappy that Barnes/Jones did not develop/get healthy enough to make Wells expendable, that the Rams did not take a more proactive approach in the offseason to solve the center position, unhappy that Wells will probably miss most of the season with injury, and I don't think he's very good even when he plays. Realistically the Rams were stuck with making a play for Mack or drafting a center higher, so I accept Wells is the best we could do, but doesn't mean I'm happy about it!