FYI, structural engineering is a very exact science. All materials WILL deflect under load. That deflection depends upon the amount of the service load and how it is applied, the shape of the member (section modulus) and the modulus of elasticity of the material. In "properly designed" members the deflection is within tolerance that is specified. That is generally dependent on the intended usage of the member. If the service load is half, then the deflection is about half. The deflection is generally calculated at the design capacity of the member.
Tom, if your bench only deflects a mm, then your bench is probably way too strong for the intended purpose and has never been close to it's design capacity. And that is a good thing.
The trick is to be able to predict or define what the actual service load needs to be.

Bill,

They don't deflect even that much. But I wouldn't call it "way too strong." They need to remain flat in order to do the jobs I perform on them. Same with a good woodworking bench - you don't want it to deflect by any easily measurable amount or the items you construct on them won't be square and true.

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Tom, in that case the bench needs to be way stronger, just to satisify the need for flatness.

Agreed. And it's possible to get that strength and rigidity without going to extremely heavy materials or bulk. I have 2 benches made with lightweight torsion box construction that you can walk around on without creating enough flex to easily measure. But one person can pick them up and move them about.

Of course if you need the bulk/mass, such as when mounting a lathe that is expected to turn heavy, out of round pieces, then it's better to utilize heavy, thick, timbers or structural steel to obtain the required strength.

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Man, this is so much like rod design. So many parameters and conflicting criteria. Strength does not have to mean self weight. Hollow sections work very well, because the material in the center does not contribute very much to resist bending and/or deflection and can be very light indeed. I have a very old book that is dedicated to woodworking benches and most of them are extremely massive because they were using hand tools, i.e., Roy Underhill's stuff. Glad we are not still using wire and solder on guides on steel rods anymore.