COALESCE function

Hello All,

Attempting to select two different column types with COALESCE returns
this error:

ERROR: COALESCE types smallint and character varying cannot be matched

Attempting the same thing with a CASE statement returns a similar error:

ERROR: CASE types smallint and character varying cannot be matched

I also checked Oracle's NVL command, and it throws a similar error.
Clearly, I'm not supposed to intermix two different column types into a
SELECT statement. This is because the engine needs to return a set
given the criteria, and it's difficult to do that with criteria that
/depends on the data/, yes?

Could someone explain a/the more formal reason why I can't do what I'm
trying to do?

The relevant part of my SELECT statement:

SELECT
...,
COALESCE(f.number, f.name),
...
FROM
...,
field AS f,
...
WHERE
...
;

f.number ∈ SMALLINT
f.name ∈ CHARACTER VARYING

Thank you in advance!

Kevin

P.S. If something gets lost in bit/encoding translation, ∈ = "Element Of"