Is there a difference between Signed and Unsigned LEB128, when *encoding* the number? - encoding

Question

I understand that LEB128 decoders need to know whether an encoded number is signed or unsigned, but the encoder seems to work identically either way (though Wikipedia uses distinct functions for encoding signed and unsigned numbers).
If positive numbers are encoded the same way in Signed and Unsigned LEB128 (only the range changes), and negative numbers only occur in Signed LEB128, it seems more sensible to create a single function that encodes any integer (using the two's compliment when the argument is negative).
I implemented a function that works the way I described, and it seems to work fine.
This is not an implementation detail (unless I've misunderstood something). Any function that can encode Signed LEB128 makes any function that encodes Unsigned LEB128 completely redundant, so there would never be a good reason to create both.
I used JavaScript, but the actual implementation is not important. Is there ever a reason to have a Signed LEB128 encoder and an Unsigned one?
const toLEB128 = function * (arg) {
/* This generator takes any BigInt, LEB128 encodes it, and
yields the result, one byte at a time (little-endian). */
const digits = arg.toString(2).length;
const length = digits + (7 - digits % 7);
const sevens = new RegExp(".{1,7}", "g");
const number = BigInt.asUintN(length, arg);
const padded = "000000" + number.toString(2);
const string = padded.slice(padded.length % 7);
const eights = string.match(sevens).map(function(string, index) {
/* This callback takes each string of seven digits and its
index (big-endian), prepends the correct continuation digit,
converts the 8-bit result to a BigInt, then returns it. */
return BigInt("0b" + Boolean(index) * 1 + string);
});
while (eights.length) yield eights.pop();
};