Its not going to be easy, but you can eliminate United BE from your search by hitting the bags tab on Google Flights and adding a carryon bag. United BE disappears.

Then you just have American and Delta left. Then pick one, and take off the BE option up top and you get your price. Pick the other and you get your price.

I am not going to stop traveling because there is an extra step in the search. Maybe its because I started traveling before there was an internet and, back then, you used to have to have a flight book and call each airline and ask for their price.

In light of that, a few extra clicks seems pretty trivial. So, no, I definitely have not stopped traveling because I have to click my mouse a couple more times.

As for overseas travel, my caveat is J class lie flat or stay home, so BE fares don't even impact my search.