I don't see more than a bunch of accepted payment methods anywhere I
ever been in my life, I don't see merchants trusting more than a handful of
third parties.

Sure. I buy this. Although the credit card market is a great example of what we don't want: a stagnant duopoly of trusted third parties who rampantly abuse their position. So I'd hope we see either (a) nobody really caring about this BIP because Bitcoin gives good enough double spend protection or (b) lots of anti-double-spend providers (hundreds seems fine).
 
Ultimately you care because the alternative is to wait.

No, I will never wait. Neither me nor the merchant wants to me to be pointlessly hanging around for an hour. The alternative is to pay by credit card or cash. Outside of experiments there is no such thing as a shop that only accepts only Bitcoin and will require me to wait for a block because I didn't use a TTP to guarantee anti-double spends.
 
So this seems like a fundamental problem to me: having the ability to say, "here is a proof I won't double spend" is fine, but it doesn't achieve anything if the merchant would have sold me the goods in return for a normal Bitcoin tx anyway, which in practice they always will because this system starts out from zero users and would have to work upwards. I especially will never use this system if I have to pay for it - I'd much rather just put my money into a wallet that can't generate these proofs and pay the sticker price.

Maybe what this BIP needs is an extra field that lets the merchant say, I will give you a discount of X satoshis if you give me a no-double-spends proof. In other words invert it: the sticker price is what normal Bitcoin transactions cost, and then your wallet shows you the regular BIP70 price minus the discount plus the third parties fee as what you finally pay. I compare it to the sticker price the merchant is asking and if it's lower I'm happy, and if it's higher my wallet would automatically avoid using the TTP because I don't want to ever pay more, only less.

The market would then figure out if the fees the TTP charges are worth the lower losses due to double spending fraud.