Because few chemicals can affect the Mesh, their tactical application is limited. Today's chemicals are just one more obstacle to manned warfare on the battlefield. The low chances of a breakthrough chemical weapon mean the current calculus of uncertain effectiveness and certain retaliation will persist. Hitting U.S. civilian targets requires the use of strategic delivery vehicles. The few who may get them would not waste them on chemical weapons if nuclear ones are available.
Biological weaponry is even harder than chemicals to use tactically.
Germs are hard to control and may backfire as gas did when first used in World War I. Their effect on humans is extremely difficult to test. The more open the world, the harder it will be to hide errant tests. Greater sophistication could lead to greater disaster. Anthrax, for instance, is very potent, but infected areas are uninhabitable to friend or foe for eons. Germs that kill their host quickly will not spread quickly.