Why is it an unwanted thing? By the same logic that demands "self" to be explicit, if you don't specify "self", then you explicitly don't want the method to be an instance method - seems very straightforward to me. And it's still invokable via instance member access, so the user of the class is none the wiser. Where's the footgun?
My complaint is of course more complicated than the syntax alone. I'm just saying that a distinctive syntax for self-as-receiver could be used to drive other changes that would make things more intuitive and self-consistent overall. And, of course, any discussion about "elegance" is going to be inherently subjective.
With respect to commonality of various constructs - this is all from personal experience writing Python code (for a project that is hosted on GitHub, by the way). It doesn't require particularly fancy code to trip that wire in general - it just requires code that tries to be generic, i.e. not make more assumptions that it needs to about the types of values that flow through it. Python classes break that genericity by treating functions, and only functions, in a special way whenever they flow through class attributes. This is particularly egregious in a language where every object is potentially callable, and non-function callables are very common; so functions really aren't all that special in general - except for that one case.
With partial() specifically, of course you can avoid that in this manner. But why would you, if it works with regular functions? I prefer it over defs, not just because it's more concise and avoids repeating things, but because it's also clearer - when you see partial(), it immediately tells you that it's a simple alias, nothing else.
But regardless, it's a function that has a certain documented behavior, and common sense would dictate that this behavior works the same for methods as well as functions. That it doesn't is not an intentional limitation of partial() - it's an unfortunate quirk of the design of methods themselves. And if you don't know exactly how functions become methods in Python, you wouldn't have any reason to expect the behavior that it exhibits. That's why the docs for partial() have to spell it out explicitly: "partial objects defined in classes behave like static methods and do not transform into bound methods during instance attribute look-up" - because that's not a reasonable default assumption!
The bigger problem is that every library that offers a generic wrapper callable has to add the same clause to its docs, because they're all affected in the same way. And if they don't document it, and you use, say, a decorator from a library - how do you know whether the fact that it returns a function and not some other callable is part of the contract that you can rely on, or an implementation detail? Conversely, whenever you implement a decorator, you have to be cognizant that changing the type of the return value from/to plain function can be a breaking change for your clients - and that is even less obvious.