Pretty much.

Of course it depends on what you mean by "kosher."

The most common full traditional system also extends to dinnerware and cookware.

A dish, pot, or utensil that had in the past contained hot meat food is believed to have absorbed the "taste" or essence I guess of meat and thus cannot be used with any hot milk food.

Then you also have to look for hekshers even on dairy and pareve (neither meat nor dairy) foods because  they might have been made in factories/kitchens that also process meat, pork, etc. Restaurants also have the same problem.

Being a vegetarian frees you from the insanity of having two sets of everything and keeping meat and milk altogether apart.

You're welcome.

Although FWIW, I don't believe in magical mystical invisible meat and dairy particles contaminating cookware.

The Torah says don't boil a baby goat in its mother's milk. OK, fine. I can't imagine a situation where I would ever actually do that, but OK. The rabbis expanded this to prohibit creating, eating, or otherwise benefiting from a mixture of meat and milk. OK, fine. There was disagreement, however, whether poultry -- which cannot be boiled in its mother's milk -- was included in this ban. Erring on the side of caution, the majority opinion was yes. I don't agree with that, but I can see that it makes sense.

But when one expands that to prohibiting the use of cookware that was in contact with meat in making or eating a dairy dish or vice versa, that's where I think one starts moving into OCD territory.

I cannot taste meat or milk residue on a spoon or in a pot. I cannot see meat or milk residue on a poon or in a pot if I have done a decent job cleaning it. If you blindfolded me and switched a "fleyshig" pot with a "milkhig" one I would not be able to tell the difference. Therefore, I really can't see much sense in the matter. The whole thing is too reminiscent of "cooties" for my taste.