There is nothing inherently wrong with the term Warrior. Many Militaries have successfully integrated the idea of the "Warrior" in to their Military culture.
New Zealand is a great example of this. The Maori warrior culture is very important to not only their Armed Forces but also their Nation as a whole. Is it surprising that they have a far better relationship and integration with the large Aboriginal population in their Country than we do with ours?
There are other concepts like Bushido in Japan, Chivalric Code in Europe, Eso Ikoyi in Africa, Futuwwa in the Arab World that have been used quite successfully to integrate a Warrior Culture in to soldiering and the Military.
Your assertion that warriors have lost to professional soldiers throughout history is also wrong. It's such a North American viewpoint and has more to do with projecting our own insecurities concerning our history than it does with the actual validity of the term Warrior.
I basically consider it a thinly veiled form of North American racism that actually denigrates Native American/Indigenous Warrior culture.
I'm certain Custer wishes he and his "professional soldiers" took the threat from the warriors at little Big Horn more seriously.
Anyone who has a problem with the term Warrior needs to get over themselves, stop focusing on their own insecurities and focus on the positive aspects of a Warrior culture and there are many.