Is inversion always cheap with Twisted Edwards curves? I'm reading on Jubjub, which is planned for the next upgrade of Zcash. It is based on a Twisted Edwards curve with parameters $a = -1$ and $d = −(10240/10241)$. The reading says Jubjub does not need projective coordinates because inversion is cheap.

My question is, is the "cheap inversion" property that of Twisted Edwards curves in general, or the parameter selection of Jubjub in particular?
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.