SQL / PostgreSQL left join ignores “on = constant” predicate, on left table

Question

An SQL left join query ignores an ON column = constant predicate on the left table.
However, it cares about another ON column = cons

Answer 1

The point is that the ON clause for a LEFT [OUTER] JOIN only regulates whether a row from the right table is joined.

It does not filter rows from the left table. If you want to do that, the expression has to go into a WHERE clause (as you found out already) or the ON clause of a [INNER] JOIN.
That's all by design.