You already saw my related answer addressing the reverse conversion timestamp → timestamptz without table rewrite:

• ALTER timestamp column to timestamptz, without "converting" data?

Well, since Postgres 12 the same "easter egg" feature applies to timestamptz → timestamp as well. The release notes:

Allow ALTER TABLE ... SET DATA TYPE changing between timestamp and timestamptz to avoid a table rewrite when the session time zone is UTC (Noah Misch)

In the UTC time zone, these two data types are binary compatible.

So just:

SET timezone = 'UTC';  -- unless already set to UTC
ALTER TABLE tbl ALTER COLUMN ts TYPE timestamp;
RESET timezone;       -- optional

And you don't have to mess with system catalogs directly (which should be avoided if at all possible).

You already saw my related answer addressing the reverse conversion timestamp → timestamptz without table rewrite:

• ALTER timestamp column to timestamptz, without "converting" data?

Well, since Postgres 12 the same "easter egg" feature applies to timestamptz → timestamp as well. The release notes:

Allow ALTER TABLE ... SET DATA TYPE changing between timestamp and timestamptz to avoid a table rewrite when the session time zone is UTC (Noah Misch)

In the UTC time zone, these two data types are binary compatible.

So just:

SET timezone = 'UTC';  -- unless already set to UTC
ALTER TABLE tbl ALTER COLUMN ts TYPE timestamp;
RESET timezone;        -- optional

And you don't have to mess with system catalogs directly (which should be avoided if at all possible).