By that logic, the NY Times should be banned as a source. They're opinion section is chocked full of basically the pro US point of view and defending Israel (including a memo advocating genocide denial). One-sided coverage, poorly sourced, nakedly biased, it all applies to them, too.

Allowing sources from all points of view, as long as the facts are true, seems better than picking and choosing due to bias. Even these "centrist" institutions have their own biases.