As far as I'm aware, there's no winner for cooking. I've never seen a recipe that required temperature more than as a value that could be provided in any units as long as you have equipment in those units (i.e. I'm not doing math with them). Putting "400°F" or "200°C" or "475 K" or some arbitrary "oven level 5" into my oven shouldn't really change how it comes out.
On the stovetop, I've never had an instruction with a temperature attached besides "interior temperature must reach X" or keeping something at a near-boiling temperature, which I've never needed a thermometer for, and 90% of the time I'm improvising without caring what the temperature is outside of "hot enough to cook the way I want but not too hot".
Sous-vide? It needs the temperature within a tight range, but the scale attached to the numbers doesn't matter as long as it's the one my thermometer uses. Double boiler? Doesn't even need you to use a thermometer to keep the temperature right. Give me a kitchen with everything in unpronouncible alien temperature units and I'd do just fine.
Can you elaborate on the cooking though? I've seen that mentioned here a couple of times, and I'm not sure I follow. I'm from a Fahrenheit country and my wife from a Celsius country, and it's never caused any issues or confusion in the kitchen. But maybe you mean also for the volumetric measurements as well (or primarily)?
But there is something else, and I am asking you the question. Since you and your wife live in countries with different unit systems, isn't problem when doing each others recipes?
I mean I live in Europe, and if the recipe calls for 4 ounces of butter, I don't have a 4 ounces stick of butter, I have a 125g stick, which is not exactly that. A quart of milk is not exactly the liter I have. And my oven doesn't do 350°F, it does 180°C which is not exactly the same. In the end, I will have to adjust the recipe to my standards, and things may be lost (or gained) in translation, but it won't be the same.
Not really. Celsius maps to the boiling and freezing points of water in Paris. Live in Denver and you're screwed. And -- this is important -- nobody measures the freezing points and boiling points of water, because during its phase changes water holds to that temperature automatically.
Fahrenheit is also twice the resolution of Celsius. This is highly advantageoous for body temperature, medicine, cooking, and other functions. Celsius's integer resolution is horrible.
As for body temperature the rule of thumb as I know it is sth like this:
36 - fine
36.6 - the theoretical perfect temperature (but it's a lie [1])
37 - observe
38 - go see doctor (but no rush)
39 and higher - go see doctor immediately
As for "requires medicine" - I don't remember having to make that decision, if I had 38+ C fever I just went to a doctor anyway.
[1] the actual perfect temperature changes by almost 0.5 C between people, time of day, time of month (for women) and other factors (measurement error). If you used thermal method of anticonception you'll know how variable it really is.
Feet or inches are, I think, a bit more human friendly than meters, but only when used by themselves, that factor of 12 is just weird in a base 10 system. I know that the argument is that you can divide by 3 and 4 easily, but when it matters, metric countries simply make standard sizes a multiple of 12 (ex:120mm).
For volumes and weights, I find absolutely no redeeming feature to the imperial / US customary system. The kilogram is a perfectly fine unit, so is the liter, and that both are the same when we are weighing water is a very useful property. Because many things are around the density of water, you know that most things that fits in a 1L bottle weight around a kg, and you can often measure volumes with a scale without conversion.
Metric is not the most practical for every single situation, but it is more practical when used as a whole, that is, when you need to deal with with several quantities at the same time (ex: masses and lengths). And there are everyday situation where it is simply better in my opinion, like cooking.