Polluting every type with it is just a very bad implementation which has nothing in common with the concept of NULL as proposed by Tony Hoare in the paper "Record Handling".

The concept as proposed by Hoare is strictly necessary for things like partial relations, which are encountered very frequently in practice.

It is true however that a large number of programming languages have misused the concept of a NULL reference proposed by Hoare.

As you say, there must be distinct types that may have or may not have a "nothing" value.