Simulation
Bullwhips are not good weapons. They cannot leave any lasting damage; a lash against bare skin can be extremely painful, and draw blood, but it cannot break bone or even cause deep wounds. In theory you could bleed someone to death, but it would take ages. The only real chance was psychological: overload your target's ability to cope with the pain. Against a target who can ignore or not feel that pain (certain drugs, an extremely rare genetic defect, pure grit), a bullwhip cannot do very much. And even regular, albeit heavy clothing could make it very difficult to get a real lash. Maneuvers to trip or disarm a person with a bullwhip are possible, but very difficult.
Dungeons & Dragons 3.x can't model all that very well; damage is heavily abstracted so "pain" is too fine a detail to get into, much less overwhelming pain. So nonlethal damage is used, even though bullwhips cannot forcibly knock someone out. And any armor bonus makes you immune, which is probably the most reasonable restriction on them. They can be used to trip or disarm, which is realistic enough, assuming fantasy heroics.
But then they cannot threaten. This, from a simulation perspective, is nonsense. The only real advantage a bullwhip provides is that it moves very, very suddenly, is almost impossible to visually track as it is twirled, and has enormous reach. That's why it is used to control animals: you can stay well out of their reach, you can't actually injure them, but they don't know that and the lash is very painful. Against a human opponent, he can run right to you: you'll get several free hits, which will hurt a great deal, but if he keeps charging there is little you can do about it.
This works almost exactly like an attack of opportunity. Actually, you wouldn't even get as many AoOs as you might get attacks in reality. So the whip not threatening is absolutely unjustifiable, from simulation's perspective.
Balance
Tripping is one of the very few actually-kind-of-effective tactics that 3.x melee has access to. By tripping on AoOs, you can make it very difficult for many enemies to maneuver around you. Hardly impossible (Tumble avoids AoOs, magical flight cannot be tripped, teleporting avoids the problem altogether, plus bonuses vs. trip are common and can be large), just somewhat difficult, but that's about the best melee can do much of the time.
Since you rely on AoOs to be effective, having a large threatened area is important to you. Thus trip weapons with reach are valuable. The go-to weapon is the Guisarme: martial, trip, reach. The Spiked Chain is an option, for its continuous reach, though simply taking a hand off your Guisarme to trip with an unarmed strike works nearly as well, and doesn't cost a feat. In Core, for a Fighter, the lack of worthwhile feats means Exotic Weapon Proficiency for the Spiked Chain is only a matter of time, though Combat Expertise, Combat Reflexes, and Improved Trip are all much higher priorities. But even in Core, you're better off multiclassing out of Fighter, and then you might not get Spiked Chain until high levels, if at all. And out of Core, there are just better feats to take. It's not bad but you can do better.
So how would a Whip stack up if we houseruled it to threaten? Greater range, which is certainly valuable. But the damage is basically nonexistent, and you cannot take more than one AoO per provoking action, which means for anyone who would have to go into the regular reach's range is taking exactly the same number of attacks as he would with a Guisarme or Spiked Chain. So the only time the reach matters is if the enemy has to leave a square that the Whip threatens without having to do the same from a square the Guisarme or Spiked Chain threatens. That will come up but not all the time: it's not all clear that this is worth giving up basically all damage, plus possibly a feay if we compare to the Guisarme. For some people it might be, but for a lot of people, the damage will be a lot to lose (after all, you still have to pump Str for trip checks), and they may not have the feats for it.
Which would make it a balanced feat. It's useful, but not at all must-have. Wizards made a trend of usually overestimating the abilities of melee characters, and underestimating how great a cost a feat can be. As a result, they were overly conservative, particularly early on, with the power level of feats. And Paizo copied their Whip and inherited some of these problems, and throughout Pathfinder have demonstrated an even stronger trend to never give melee nice things.
