A Floyd Rose is a whole system, and only works correctly when the whole system is used. Remove any component and the integrity of the system is compromised, and you're left with just a regular old, non-locking tremolo system.
The NFT Floyd that GG uses, or the Wilkenson with the locking saddles that Pete Thorn uses might stay in tune marginally better than a Gotoh 510, but only marginally. I promise you they won't stay "Steve Vai" in tune like a Floyd-style double-locking system does.