This is part of the charm of this thread hearing what is most important to each cook.
Do you think it’s the same pan? I’ve had it a long time and don’t know what it’s called, but it is Calphalon. I’ve never thought of using it for stir frying!
No, mine is more wok-shaped, the rim is different, and the lid is glass.
I’d go with a copper sauteuse rather than a rondeau. I more often tilt the pan for sauces (which is easier in the sauteuse than in a rondeau) than transfer to the oven which is easier in the rondeau than sauteuse.
Yet my most commonly used pan at home is a 12” steel lined copper skillet.
Kenji might pick a Wok.
I always had thought that a fait tout was a large Windsor shaped saucepan, but the name’s been applied by so many cookware manufacturers to so many things it’s become kind of a red flag in my mind (maybe they should call these gotta-haves “fait rien” since they don’t really excel at anything). I guess if I was stuck with one pan it would be a rondeau; I was very fond of an anodized aluminum original Calphalon/Commercial Aluminum Cookware shallow 5 qt soup pot with a 2 handled lid that could be used separately as a shallow pan (not a grill pan) that I had many eons ago- probably a wee bit deeper than a pommes Anna pan, but the same sort of set up as to the lid. I know that lid-as-a grill braiser sand Dutch ovens are available in ECI, but that wouldn’t be my choice of material for one pan only.
You actually post a tough question. The short answer is that there is a pan that does it all, but probably not great at any single task too. To me, it is the same as most tools. The cooking pan, or knife, or car which does it all is the tool which does not specialize and therefore not great at any of the tasks.