When UNIFIL's current force was put together in 2006, the US and UK were stuck in the quagmire of Iraq's civil war. As a result there was no question of their being involved. In general, countries with powerful militaries avoid contributing to UN forces. 7/

With absolutely no disrespect to Ireland, Spain and Sri Lanka, these armies have less ability to operate in a robust manner than would a force from the United States. But of course the US would not want to risk its forces having to face down Israel's. Again, not a UN choice, but a national one. 8/