Steel support bars needed for desk or not?

I',m building a couple of 120cm long, 65cm deep and 27mm thick desks.
The top is solid oak stave.

One side is supported by drawers, the other by hairpin legs.

Any thoughts on adding a flat bar steel support at the legs end on these for stability? Needed or not? And if so, what kind of length? I'm thinking it would be screwed on front to back (ie perpendicular to the front of the desk).

Grateful for opinions!