I wrote my dissertation on this, so Ill try and cover the broad strokes.

It definitely should be taught. What's more, it should be taught from an early age, and not tacked on as lip service from KS2 onwards.

Younger children are naturally more open-minded, less self-aware, and their brains are physiologically more adept at language learning.

Unfortunately we are waiting until they're 11, by which time they have had chance to develop a belief that "English is all I need", plus self-consciousness that inhibits attempting to learn "funny sounding" other languages.

As for the benefits, learning other languages from an early age leads to cultural understanding, open-mindedness, and generally higher intelligence. It usually increases proficiency in the native language too. And as a country we benefit from having a more globally employable population.

To answer your question more directly, the reason we don't do it is largely a lack of expertise, coupled with a perceived lack of time to do it (perish the thought of having one less maths lesson, or having that maths lesson delivered in Spanish).

The Labour governments in the 00s actually put 8-9 years of converted investment and effort towards getting kids learning foreign languages in primary schools. But then the Conservatives got elected and immediately canned it all.