I feel completely the opposite.
Wait, not on the getting tested regularly part -- I'm all for that. I'm an every three months gal myself. But as far as discussing or showing STD testing results with a client/provider? No way!
If someone showed me his STD testing results, I'd apologize that he misunderstood the nature of our meeting, return his money, and leave. If "What sort of condoms should I bring?" would be an LE red flag for you, why wouldn't discussing/trading STD testing results be the same? If the police want to arrest you for engaging in prostitution, they pretty much will, but don't make it even easier for them.
There's also the personal security risks of handing someone sheets of paper with your full name, address, doctor's office, etc. on them (especially a risk for the ladies, who don't regularly give out that info as clients may have already done for screening). Besides, as others have mentioned, they can be forged. And lastly, you can be infected between the time you're tested and you get/show the results, or at the time of testing you could have been in an incubation phase and therefore showed negative, so as far as an "I'm clean RIGHT NOW" proof ... that doesn't really exist when you're having sex with multiple partners.
In short, nice idea, but ultimately useless and not worth the risk.
Edited to add:
Here's a link to a site with the typical incubation periods:
http://www.stdresource.com/concern/c1_d_3_a.php