I think that the proposal was not that the team definitely pay the extra $8M, just that the amount that the contract was under market would count separately against an independently calculated luxury tax number.
So, let's assume (for sake of argument) that the Heat "big three" contracts all start at $13M per year, but that all three guys were offered $16M per year from other teams, that they declined - that $9M difference would then count towards the Heat's luxury tax figure (though not the salary cap figure or actual payroll). Currently the luxury tax is right about $70M, but the "savings" on their big three would put the Heat's luxury tax line effectively at about $61M.
Essentially the suggestion would allow teams to "underpay" for players, but the luxury tax would be based on the true market value of those players, which would add at least some discouragement to stockpiling players at below market value. I don't even think it would be terribly much discouragement, as a team could "underpay" its players to stockpile talent under the salary cap, then pay back some of the savings once (if) they exceeded the tax. It would be better than nothing, but I can't at all see a proposal like this killing free agency. The danger would seem to be in teams making outrageous offers to free agents just to spite their eventual targets, but you'd have to keep in mind that the player might actually accept the outrageous offer. But if you set up reasonable rules - can't make an offer that you can't legally make given the cap, outstanding offers which become illegal due to the offering team adding salary get rescinded automatically, etc. - I think it would be pretty easy to get a rule like this established. I can't see the players losing much, so I don't know why they would complain.
The more I think about it, the biggest problem is that it doesn't seem to have much in the way of teeth. Currently, rich teams can underpay to get under the salary cap and continue to stockpile talent. Under this proposal, it's no different, except that the rich teams might have to pay a little money at the back end in tax. But the real deterrent to this sort of stockpiling now isn't the total cost, it's staying under the cap. And this proposal doesn't change that.