Why is this not an obligatory war? (I mean in times of war, not regular service.)

First of all, without training in peacetime there is no way to serve in war. So that is at least preparation for a commandment. Would you imagine not building a sukkah because there is no commandment in that, and then arriving at the festival with no sukkah to sit in?
Beyond that, regular service is part of the war. There is a war on terror, defense of the borders, and deterrence. We are at war all the time.
But in my opinion, a war of this kind is not a commandment in its usual formal sense. No more than enlisting in the Belgian army if Belgium is under threat. It is an obligation of a citizen to his state. Even Maimonides’ list of the three obligatory wars, one of which is helping Israel against an oppressor, is not really an obligatory war like the other two. It is the law of preservation of life on the collective plane (“Shall your brothers go to war while you sit here?!” Moses does not tell them there is a commandment; he challenges them morally). On the individual plane, when someone threatens you, do you have a ‘commandment’ to defend yourself? You have the right and the duty to defend yourself. That may be a ‘commandment’ in some personal sense (“and you shall live by them”), but it is unrelated to obligatory wars, which are communal commandments for the sake of a commandment. See Bartenura on Sotah 8:7, who calls this a discretionary war. In general, there is considerable doubt whether an obligatory war can be defined without a king, a Sanhedrin, and a prophet. The decision about an obligatory war belongs to the king alone, but the appointment of the king is by a Sanhedrin and a prophet.
But as I wrote, the discussion of whether this is a commandment or not is not important in my view.

I’m continuing to ask, even though you think it isn’t practically relevant, for the sake of the halakhic discussion of the issue.
This is a general difficulty with the decision to include helping Israel against an oppressor as an obligatory war. You also agree that this falls under the definition of helping Israel against an oppressor, right? (Indeed, Rashi at the beginning of Sanhedrin said that only Joshua’s war is an obligatory war. I once heard a lecture that wanted to explain that the dispute between Rashi and Maimonides depends on whether an obligatory war is defined by whether one performs a commandment in the act itself (Rashi), or whether the commandment lies in the resulting outcome (Maimonides)).
Seemingly, you need a prophet and a king for a discretionary war, no? Consultation with them, as best I remember, is mentioned in Jewish law only in the case of a discretionary war.

It seems you didn’t read what I wrote. So why am I writing at all?