I think the whole point of being a successful rich democratic world power is to spread good things around the world, particularly when you don't have strong interests (like Ukraine). Helping democracies struggling against authoritarian regimes should be a must, particularly in the case of Armenia, that most certainly would cost a fraction of the US budget (for comparison, the much larger Ukraine war costs 10% of the U.S. Department of Defense budget or 0.3% of the U.S. GDP)

Azerbaijan is a petrostate that exports through Georgia and Turkey a lot of oil and gas to Europe. That said, their oil production is like 500k barrels of oil per day, it's like 0.5% of total worldwide consumption.

The equilibrium of forces there means that a coalition of unexpected allies helps the autocratic Azerbaijan: Israel helps Azerbaijan because of their feud with Iran, Turkey helps Azerbaijan because Azerbaijan is also ethnic Turkish, and Brussels helps Azerbaijan because of their oil and gas imports (particularly more important since the 2022 invasion of Ukraine)

This means that the much more democratic, but poor Armenia was left with Russia and Iran. But Russia isn't helping Armenia anymore since the 2022 Ukraine war, where Russia declined to protect Armenia under their Article 5 equivalent.

What Azerbaijan is doing in Nagorno-Kharabak is terrible and it's even worst to realize how much Brussels and to a greater degree Washington are closing their eyes. They put Armenina in a position to need to allied with Western enemies, but now their own ally is doing genocide against Armenians.

Washington doesn't have much interests in the region, their only interests are because they babysit Europe. Why they don't mark a line in the sand and side with the democratic Armenia? Isn't that the whole point of being the leader of the free world?