“Hmm how should I get to work tomorrow? Normally I’d take the car, but after adopting a stance of distractive pedantism I realized that a car isn’t an acceptable solution to my transportation problem.”
Like please explain what definition of solved you are using. It’s not one most people would be familiar with.
The fact that we don't have a better solution now is why it's worth researching. We only have modern cars because we didn't consider transportation "solved" when we had horse-pulled carriages. Many people are looking for better solutions right now, because we believe they certainly exist.
Isn’t that true of everything? There may always be something better in the future. It’s ridiculous to say that we can’t have solutions to anything in the present because there may be better options in the future.
No, that is not true of solved problems and solved games in the mathematical sense, which is what we're talking about. E.g. tic-tac-toe is a solved game, no better solution can be devised.