Why does Enumerable.Single() iterate all elements, even when more than one item has already been found?

You didn’t seem to be the only one thinking that. The .NET Core implementation has an optimized version:

using (IEnumerator<TSource> e = source.GetEnumerator())
{
    while (e.MoveNext())
    {
        TSource result = e.Current;
        if (predicate(result))
        {
            while (e.MoveNext())
            {
                if (predicate(e.Current))
                {
                    throw Error.MoreThanOneMatch();
                }
            }

            return result;
        }
    }
}

So to answer your question: there doesn’t seem to be a ‘good’ reason, other than just a developer not thinking about optimizing this use case.