Why don't race bikes have solid front triangles?
Much of this is due to UCI regulations. They specify what shape and size of frame can be used. It is not allowed to add extra parts just for improving aerodynamics.

See the UCI document Technical Regulations For Bicycles - A Practical Guide To Implementation (PDF) which covers most of this.

As it says for Article 1.3.020, the frame elements must be tubular, with a maximum transverse dimension of 8 cm and a minimum transverse dimension of 2.5 cm, in a maximum ratio of 1:3. Also Article 1.3.024 "Protective screens, aerodynamic shapes, fairings or any other device that is added or forms part of the structure, and that is destined or has the effect of reducing wind resistance, are prohibited."

It could be possible to make a more aerodynamic bike that was not allowed by the UCI. But you would be restricted by what races it could be ridden in. A few brands have mode non-UCI compliant race bikes, mostly designed for triathlon. eg some versions of the Specialized Transition or Shiv, which have extra aerodynamic tubes etc.