A motorhome with good brakes could (probably) stop a towed vehicle without auxiliary brakes, adequately during "normal" driving. The problems occur during panic braking, when you might be swerving and braking to avoid something, or just trying to stop in a hurry - especially when descending grades. Now, there are several thousand pounds of additional weight pushing hard on the rear of the coach. If it's pushing at angle, who knows where the towed vehicle is going to end up, or if it will even stay attached to the RV. And if it does break free...
If you live out west, and you regularly climb and descend a lot of grades, you really don't want all that extra weight pushing full time on the RV's brakes. Proportional braking from an auxiliary brake is a big help.
Like Gary said, it may be technically legal in some states to tow a vehicle without an auxiliary brake, but it's a bad idea to go that route, just to save some money. If you're going to tow, please invest in an auxiliary brake.
Kev