Just speaking as an engineer:

Curved tubes have more length, hence more mass = weight.

Curved tubes are more flexible than an equivalent straight tube of the same material, construction, and dimensions.

If there are high compression loads, the curved tube should buckle (i.e. become destroyed) with less axial force than the equivalent straight tube.

If the curved tube is metal and has been given its curvature by bending, it has already been cold-set one time more than the equivalent straight tube. This means it is closer to its final failure.

The same problems exist with composite tubes, but there is the option to add material or optimize the use of material (asymmetric layup, or control of fiber direction) to manage stress distribution. But this has to add weight and cost compared to a straight tube intended to satisfy the same purpose.

I don't see any benefits to curved bicycle tubes other than aesthetics (the Hetchins) or in some cases providing a degree of bump absorption (curved fork blades).