I don't see how TT value being shown affects free trade, all it indicates is cost of materials used to craft it to full value, or fully repaired value if UL. It is what it is.
At most it gives you an idea of whether you should go craft your own or pay at least the start bid. The seller can already 'propose' both start bid and buyout, so their view of the expected value is already indicated.
If we turn the whole thing into guesswork the greedy will dominate, and those who cant be bothered with mindgames will TT more than they do now, or will simply sell through spamming trade channels.
TBH the basics of the AH are sound but not without room for improvement.
1. Let us use the pec as well as ped when setting SB and BO This will help stop inflation on low value items and stacks, where 1 ped pushes the MU over the norm
2. Revise the whole sales history charts. Make them show individual sales (not averages) and let them also show the TT of the item sold, the tiering(if any) and size of stack (where relevant), at present the info shown is frankly misleading at best. This revision alone would make market manipulation sales stand out from the crowd.