Both carbon fiber and kevlar have higher tensile strength per cross sectional area. Kevlar in particular seems to have less torsional strength per tensile strength than steel, which should reduce inharmonicity. Why not use one of these materials in particular for the higher notes on a piano, where most all pianos end up having a "woody," or "hollow," sound because of inharmonicity?
Those materials seem to have less of an elastic range and decidedly less density than steel. Their higher tensile strength means that they have less of an elongation per force and thus less excitation and vibrational energy per force, and the force particularly of the higher strings already is a limiting factor for a piano frame.
Doesn't sound like those strings would be able to sustain a lot of vibrational energy, and that at a considerably higher force than the existing strings.
I believe the simple answer is, as often, tradition. You expect a piano to sound like a piano. Most probably someone has tried variations, such as using different kinds of strings, but rejected it as non-improvment.
You might compare with acoustic guitars, where there are two main directions: steel strings or nylon strings.
Add that the market for acoustical pianos is dwindling, there simply is not that much room for experiments.