Bitcoin requires much less trust in third parties.
However, one might imagine that a highly trusted Bitcoin org (looking at you Bitpay) could print paper denominations that circulate that are certificates of claim NOT paper wallets (perhaps even fractionally reserved) These bills could be redeemed by the holder for actual btc, making the bill then void of further claim.
I am not sure how this would be accomplished. I do think it would be extremely valuable.
Unless you count the miners there really is no third party with bitcoin. Person A pays person B with no C involved.
You dont need a bitcoin org to print certificates of claim as you call them because you can do it yourself and for free, unless there accepting btc as payment big business org can stay out of developing things to buy that we really dont need.
Money needs to be spent on better and easy wallet security, until then Trezor.