>Bicycles don't have the minimum size problem GGP is talking about.

They do, in a slightly different way. Bicycle frames are (broadly) stiffness-critical structures. Wider-diameter tubes have a higher specific stiffness because of the increased moment of inertia - that's why we use structures like tubes and I-beams instead of solid bars. Steel frames have skinny tubes, because they're limited by the minimum wall thickness of the tubing; increase the diameter too much and you have a tube that is very vulnerable to dents and very prone to buckling. Steel racing frames of the 1970s are remarkably flimsy, because framebuilders were pushing wall thickness to the absolute limit.

Aluminium bicycle frames are only lighter because the lower density allows you to retain an acceptable wall thickness on larger-diameter tubes. An aluminium frame with the same tube diameters as a steel frame would be considerably heavier than the steel frame, because an aluminium frame needs to be overbuilt to compensate for the lack of a defined fatigue limit.

All common steel alloys have essentially the same stiffness (~207GPa), but higher-strength steels allow us to use wider-diameter tubes with thinner wall sections; incidentally, this is why it's quite pointless to use an expensive tubeset in a lugged frame. CFRP obviously has immense specific stiffness, but it also allows frame designers to really optimise the geometry and use the material more efficiently.

Titanium is a really nice frame material, but it does have some significant issues in practical use. Titanium is very prone to embrittlement if there is any amount of contamination in the weld. Most framebuilders aren't capable of maintaining the level of cleanliness and the comprehensive gas purging required to produce really good welds in titanium, so it's very common to see titanium frames eventually crack around the welds.

To my mind the perfect material for a non-sporting frame was the superb Reynolds 953 maraging steel, but unfortunately it is no longer available. Reynolds 931 and KVA MS2 are still very good materials, particularly when fillet brazed rather than welded. CFRP obviously wins out in terms of pure performance, but I'm not sure that I'd ever trust an old and battle-scarred carbon frame on a hard descent.