The danger of revealing results in protective coordinates is pointed by David Naccache, Nigel P. Smart, and Jacques Stern's Projective Coordinates Leak, in proceedings of Eurocrypt 2004. As noted in comment, a concise re-exposition is in section 3 of Alejandro C. Aldaya, Cesar P. García and Billy B. Brumley's From A to Z: Projective coordinates leakage in the wild, in proceedings of CHES 2020 (which uses it in side-channel leakage attacks on implementations using projective coordinates internally, even when the result is output in affine coordinates).
In a nutshell: revealing $[k]\,G$ in projective coordinates can leak some information about $k$; that's problematic.
Slightly more detail: in affine coordinates, a point (other than the point at infinity) is expressed as $(x,y)$ satisfying the curve equation $y^2=x^3+a\,x+b$, where $x$ and $y$ are field elements. In standard projective coordinates, the same point is expressed as $(X,Y,Z)=(Z\,x,Z\,y,Z)$, where $Z$ is any non-zero field element. That becomes $(X,Y,Z)=(Z^2\,x,Z^3\,y,Z)$ in Jacobian projective coordinates.
Therefore giving a point in projective coordinate gives the point, and an extra information $Z$ that can be any non-zero field element. That $Z$ depends on how the point was obtained, and is a potential information leak.
More in detail: Assume that it is given $P=[k]\,G$ with unknown $k\in[1,n)$ as projective coordinates $(X_P,Y_P,Z_P)$, and that was computed starting from a known $G$ of projective coordinates $X_G,Y_G,Z_G=(x_g,y,g,1)$, and integer $k$, using standard formulas for point addition and point doubling, and the straightforward left-to-right exponent scanning algorithm:
- $P\gets G$
- for each bit $b$ of $k$ from second high-order to low-order
- $P\gets P+P$ (point doubling)
- if bit $b$ is set
- $P\gets P+G$ (point addition)
It turns out that there is a relation between $k$ and the final $Z_P$, and that relation is exploitable to get some information on $k$.
[I started summarizing the first article, but did not finish, sorry. Feel free to expand!]