Is inversion always cheap with Twisted Edwards curves?
In the particular case of jubjub, it will be used in a Rank-1 Constraint System(R1CS) where inversion is cheap, costing one multiplication. 

Jubjub is an embedded curve and the main purpose of developing it, is due that you can use it in a constraint system. Outside of its applications in R1CS, inversion is not cheap.

Since inversion is cheap, we can use the affine formula directly.