With the exception of drop, there aren't any free functions in the prelude (I suspected this, and a quick check confirmed it). Some traits that are applicable to nearly everything, like the associated traits for derives, From/Into, ToOwned, etc. are also in the prelude. To me, that they're applicable to just about any program someone might want to write is the reason they are present. drop, on the other hand, is not as widely applicable. I just did a quick rg "drop\(" over the directory I keep all my projects in; the only match was in standback, which is derived from stdlib. Said another way, I don't call drop anywhere at all in any of my Rust code.
Performing the same (limited) analysis for std::mem::{swap, replace, take}, there is all of one match wherein I swap a telemetry log out for an empty one. Checking for as_mut(), as_ref(), into()/::into(), into_iter(), iter(), to_owned(), to_string(), and ::from(_) yields a cumulative 607 matches (nb: not lines). This does not include fully-qualified syntax for most of the methods. For reference, these projects combine to 26,834 lines of Rust code per tokei.
Macros are a different story that really isn't applicable here, as nothing being talked about is macros.
So as I've stated previously in other threads, I suppose the reason I'm opposed to it is primarily the lack of real-world usage in the areas of the projects I have cloned locally. I also personally believe that having the mem:: prefix is preferred, but that's a style concern. I understand that other use cases would benefit from these methods being in the prelude in the same way that drop is, but ~1/27,000 is hardly comparable to ~1/44 in my real-world codebases.
Now that I am finishing typing this out, I realize that it's not really an argument against free functions being in the prelude, just that it's not used enough in my experience. But regardless, hopefully this helps somehow.
As a side note, I have excluded the rust and standback repositories that I have cloned locally from this data, as I'm fairly certain they are nowhere near representative of the average codebase.