Because the USSR used to support governments and political movements the US was trying to destroy, there was a danger that US intervention in the Third World might explode into a nuclear war. With the Soviet deterrent gone, the US is much more free to use violence around the world, a fact that has been recognized with much satisfaction by US policy analysts in the past several years. In any confrontation, each participant tries to shift the battle to a domain in which it's most likely to succeed. You want to lead with your strength, play your strong card. If, on the other hand, a conflict is settled through peaceful means, that benefits us less, because our rivals are just as good or better in that domain.
Diplomacy is a particularly unwelcome option, unless it's pursued under the gun.
The US has very little popular support for its goals in the Third World. This isn't surprising, since it's trying to impose structures of domination and exploitation. A diplomatic settlement is bound to respond, at least to some degree, to the interests of the other participants in the negotiation, and that's a problem when your positions aren't very popular. As a result, negotiations are something the US commonly tries to avoid. Contrary to much propaganda, that has been true in Southeast Asia, the Middle East and Central America for many years.