The original wording seems to have issues, but I'm not sure if this is an improvement. I think a more thorough rewording is needed here.

We say "subobject(s) of a class" in multiple places, so let's not make a single change like this. Could you maybe start by looking for all the occurrences. (E.g. in [conv.mem] we say "the subobject of D", where D is a class.

I think "class object" is generally a phrase we can use, but we'll have to look at each individual case to see how to make it fit.

The standard is generally confused about "base class" and "data member" and "subobject" and the relationship among them. (For example, you can have multiple base classes of the same type, that may or may not ("virtual") cause different subobjects to exist in any class object.)

I don't think I'd support applying any cleanup in this area in the context of an editorial issue (as opposed to a core issue).

OK, thanks, @jensmaurer! Let's close this issue then. @Eisenwave: please file a CWG issue if you want to pursue this.