Does it imply that? At least strictly as defined in a dictionary, it is a fairly non-judgemental term about cooperation:

a state formally cooperating with another for a military or other purpose, typically by treaty.

So I have to wonder whether the impression of "moral high ground" that you have comes from the fact that "The Allied Powers" is a common term used for the, well, Allies (although not the only one. See 'Declaration by United Nations' the term having been suggested by Roosevelt).

In any case, the 'Allies' was used by the Axis to refer to their enemies, collectively. Here are two excerpts from Hitler's Table Talk where he makes reference to the Allies:

When we Germans pass judgment on the Duce, we must bear all these considerations well in mind, not forgetting that, when ali is said and done, it is the Duce we have to thank for the fact that Italy is not in the war on the side of the Allies. When some aspects of our alliance with Italy appear irksome to us, let us not forget that the King and his Court have much too far-reaching powers of intervention both in military matters and in affairs of State.

The only time that our conversations lasted for nearly two days was when things were going badly in Albania, and I had to try to restore the Duce's morale. It is easy, therefore, by comparison to imagine how enormous their difficulties must appear to the Allies.

A few more examples, here is a diary entry fro Goebbels, 6 June 1943:

If we worked for storms of applause, it would certainly have had a negative impact on those in the West suffering from Allied bombing.

and from his article "The Tonnage War":

They might better keep in mind the fact that hundreds of Allied ships have been hit by torpedoes in the Western Atlantic since the U.S. entry into the war.

For this last one I was able to get the original German, which uses "alliierten" for comparison:

Besser dagegen wäre es, wenn sich die Amerikaner die Tatsache vor Augen hielten, daß Hunderte von alliierten Schiffen seit Kriegseintritt der USA.

So in sum, "allies" was used by the Axis, and it doesn't seem that there was a particular feeling that it was self-judgmental to do so.

The term “allies” only seems to imply “moral high ground” in the modern mindset because that is the way the narrative of World War II is taught in most countries today: simply put, “allies” equals “good” and “axis” equals “evil”. However, the word “ally” itself does not intrinsically carry a moral connotation. The Cambridge Dictionary defines “ally” as: “a country that has agreed officially to give help and support to another one, especially during a war”, and gives as an example: “During the First World War, Turkey and Germany were allies/Turkey was an ally of Germany.”

In other wars throughout history which are not viewed as clear-cut conflicts between “good” and “evil” the way World War II is, there have been alliances, and referring to the countries in such alliances as “allies” does not confer them the “moral high ground”. In fact, the whole matter of the “moral high ground” can be a subject for a lengthy philosophical debate, but while an alliance can be entered into for moral reasons, usually all countries view their own actions as “right” and “just” and those of their enemies as “wrong”, even though the ulterior motives for such an alliance can be later judged as immoral by others.

In other words, the term “allies” has a distinct positive moral connotation in modern use due to the perception of the “good” vs “evil” fight of World War II. I’d like to add that in a similar way, terms like “empire” and “dictator” now tend to have a negative connotation, which they did not have historically (e.g. during the time of the Roman Empire) because of how they are viewed retrospectively today.

I've always wondered why the "Allies" aren't called "The Entente" (based on the Entente Cordiale between the UK, France and Russia) and the "Central Powers" not referred to as the allies (since they formed the "Triple Alliance" of Germany, Austria-Hungary, and Italy, at least at the start).

At the start of the war wouldn't one say the war was between the Entente and the Allies?

Hi friend, I did a quick search and found this question posted a couple of years ago. While there isn't a clear answer, the thread is quite interesting.
https://www.reddit.com/r/AskHistorians/comments/1uotom/what_did_the_axis_powers_call_the_allies/