While I agree w/ your last statement, IFAs don't sign right out of the gate. If you have 15 mil to spend, why offer that up right away? Why not offer 6, and see where things go?
Basically, I agree with you in that it definently makes things more difficult, but the basic premise doesn't change. I have $x to spend in free agency, IFAs, coaching, etc.... A guy pops on the FA or IFA market, I deem what I think he's worth, what I'm willing to pay and where I have to draw the line. Under your scenerio, I might be $7,999,999 and get the message that I'm behind. Unless your last minute shopping, the guy isn't going to sign that cycle anyways, so you have time to offer the $2 more to land the guy. If you don't know that the next guy has $8mil left, perhaps your next bid is for $10 mil. You get the "your in the lead message" and then sit around and wait until he signs.
I don't think you'd even have to be cheating to know who the players in the IFA market generally are. The teams w/ low team payrolls and typically in the IFA market the heaviest, unless you're in a world where there are budget restrictions beyond the standard. I don't know if asking if another coach is going after a particular player or not is cheating, but I think most can make a reasonable guess at who's a player in the IFA market, and who's not.
To me, there are a lot more things that can be done to make the IFA market more realistic, starting out w/ eliminated the original demands. Its pretty stupid that you can spend $4 mil on IFA scouting and get lucky enough to see a guy pop w/ an $11 mil demand and know he's going to be a legit ML player, while the guy who's poured $20 mil into his IFA scouting may never see the guy. I think its kind of stupid that both draftees and IFAs are not available until after budgets are set. Washington knew last year that Bryce Harper would be at the top of the board and he wasn't going to come cheap. Many of the top end IFAs are already whispered about before the IFA signing day and many already linked to specific teams for specific dollar amounts. Changing these aspects would create much more strategy to me than knowing what another team's budget is.