What you said does matter at scale. As an alternate perspective, for an initial, smaller app, I could see the CHECK method for e.g. processing/completed providing the same correct value constraints as an ENUM or a lookup table, with more flexibility, speed and less complexity. And can be refactored later if needed.
I legitimately don’t understand why a lookup table is ever seen as adding any meaningful amount of complexity.
SELECT a.foo, b.bar
FROM alpha a
JOIN bravo b ON
a.id = b.alpha_id
The speed hit from an INNER JOIN on indexed columns is negligible, and will be dwarfed by network overhead for most places. As to flexibility, if you need a new value, insert it.
