why does const not work on pointed objects?

[Jeff Schwab]

The language enforces const-correctness for a reasonably logical
definition of that concept (ignoring const_cast and mutable for now).

Agreed. Changing the definition of that concept, e.g. to provide "deep
constness" by default (as the OP suggested), would risk the loss of the
"reasonably logical" property. I won't say that other definitions would
be "wrong," just different in a potentially misleading way.