I believe PostgreSQL does this since v11, which was released in 2018: (current is v17)

> Many other useful performance improvements, including the ability to avoid a table rewrite for ALTER TABLE ... ADD COLUMN with a non-null column default

https://www.postgresql.org/docs/release/11.0/

I think there is some restriction there, like the default can't be "volatile" - I can't remember the precise definition here but I think current_timestamp would be volatile, but any static value would not.