I agree totally. You also get the case where things are pseudo-asymmetric and not ‘truly chiral’. For example when the ‘pseudo-asymmetric’ centre is connected to 2 completely similar other chiral centres that differ in chiral center assignment (R and S), but the enantiomers are still non-superimposable and still rotate the plane of polarised light in opposite directions
Asymmetric could really be any type of centre, not necessarily chiral, or even an atomic centre, it doesn’t really tell you that you’re dealing with a chiral molecule.