Yeah, which improves the time complexity too. Plus many languages offer easy list to set conversion

It doesn't change the time complexity. Both are O(n). Your point about convenience stands, though.

Actually, if you go into fully pedantic mode, the set version is worse. Hash-based set insertion is commonly taken to be O(1), but that depends on hash comparison being O(1), which depends on using single-word hash values, which means your n is bounded by eg 2^63 (50% occupancy) or whatever. Honestly fine in practice, but hash lookup isn't "as" O(1) as indexing into an array. (ie, it requires a less realistic cost model.)

You also need your keys' length to be bounded by a constant. Otherwise just hashing everything will exceed O(n).

O(1) indexing into an array is a much bigger lie in practice than relying on single-word hash values. It breaks down much, much sooner which is why we have multiple levels of caches to try and hide this.

In reality random indexing is O(sqrt(n)) for 2D memory chips, and at best O(cbrt(n)) in our 3D physical world.

And adding two numbers is also O(m+n) where m, n is their length in bits, sure.

Does it? Set insertion is O(log n) and you need to insert n items.

Not if you use a hash set. This is expected O(n) time to de-duplicate an array of integers while maintaining the original order (more explicitly written than I normally would in Rust for didactical purposes):

    let mut hash_set = HashSet::new();
    let mut len = 0;

    for i in 0..arr.len() {
        if !hash_set.contains(&arr[i]) {
            hash_set.insert(arr[i]);
            arr[len] = arr[i];
            len += 1;
        }
    }

    arr.truncate(len);

Good point but it's not exactly a free lunch. You're trading memory for the speedup.

You can also use radix sort for what I'd like to call "fake" O(n) sort since physical hardware puts an upper limit on the hidden constant.

Radix sort generally places far more restrictions on the keys than a set would.

But to order a list is O(n log n)

In the worst case, you need to insert every element into your set to find out if there's no duplicate hence it'll take O(n log n) too

Not with a hash set - that gives you expected amortized O(1) insertion (yes, both expected and amortized). In contrast, a generalized sort is O(n log n), but you can sort numeric types in O(n).