Sql databases usually come with their own date types that are implemented with integers behind the curtains. They take up less space and are easier to sort than text fields.
EDIT: also I wouldn’t consider this egregious. If the Senior explains and the person was happy to learn something then that’s a good outcome. If they are stubborn about it, then that wouldn’t be great.
But which very likely store less information than an ISO timestamp does. (The integers stored are usually POSIX timestamps.) So, you might have to store, e.g., timezone information elsewhere. (And that might also be a good thing. It might not. It depends. Without knowing more, the DB's type is probably the right choice.)
I've seen far worse things than this done to a SQL database though…
Except that ISO-8601 doesn’t include anything as useful as a political time zone, just an offset from UTC. That’d be good if UTC offset was useful for anything, but instead it just adds to the confusion.
At least in Postgresql, it is standard practice to use timestamptz type, which saves timestamp together with a time zone. Not only it uses less space on disc, but you can do a lot of operations with it natively in database itself: sort in various ways, compare to NOW(), construct time intervals and even ensure data validity with checks.