To clarify: in one of the attacks discussed we mostly picked up a signal from the address lines - that is, we exploited the fact that AES' RAM access patterns correlate with the key.
ChaCha20 is sufficiently constant-everything (which includes not having any key-dependent RAM access patterns) that we'd probably need to pick up the data (not just address) lines. That turns out to be (mildly?) harder in this particular combination of attack target and measurement setup.
We do make appliances designed to survive (or at least strongly resist) such attacks, but admittedly we don't rely on naive software AES implementations operating on external RAM. ;-)