i towed a miata with an '04 Chevy Tahoe to 5 events cross-country on an 18' open car hauler with no trailer brakes. Never had a problem pulling it through mountains or stopping.
Now, for a comparison more along the lines of "7000lbs", I used the exact same tahoe to tow a 4000+lb lexus RX350 (packed to the roof, front to rear, with personal belongings) on the same 18' car hauler with the trailer brakes connected and had zero problems. The truck pulled it with no issues and stopped it with no issues, but having the trailer brake was absolutely necessary.