I am pretty sure a drop like that should have some kind of safety restraints, but I must say, folks have died on Matterhorn and Matterhorn and not Splash (*knocks on wood*), so who knows.
A restraint on Splash Mountain is unnecessary because guests aren't being forced out of their seats by the drop-gravity more than suffices in this case to keep guests inside the ride vehicle assuming they aren't doing anything they shouldn't be.
It's also worth noting that Splash Mountain is a log flume, and the only log flumes I can think of that have restraints are at parks operated by Disney and Universal-but you can go to Six Flags parks, Knott's, Busch Gardens, or anywhere else and you'll see them without restraints of any kind. That's not because those other parks are deficient in safety-it's because those parks are operating the rides the way they are intended to be operated. Log Flumes just don't generate sufficient negative-g forces (the g-forces that push you out of your seat) to need them.
Even most older roller coasters work under the principle that gravity is the primary restraint and any lap bar or seat belt is secondary, a "just in case" measure. Those attractions were and remain perfectly safe if the rider is riding the attraction as they are supposed to be. It wasn't until later, from sometime in the nineties, that coasters or other attractions were designed with much higher levels of airtime that truly necessitated strict, tightly-fitting lap bars/restraints for safety.
But that lack of restraints on log flumes can invite poor guest decision making and/or psychological feelings of being unsafe, which is also why Cedar Fair has removed log flumes at many parks they operate (California's Great America, Carowinds, Valleyfair, Cedar Point, and so on), even though people love log flumes-the company is paranoid about people getting out of the boats when they're not supposed to. When Cedar Fair
did build a "modern" log flume-Shoot the Rapids at Cedar Point-that had lap bars installed from day one at their insistence, there was an accident where a boat rolled back off a lift hill and flipped over with riders on board and restrained. It's a miracle nobody was killed. Although that's not the only reason that attraction is no longer operating, it certainly didn't help prolong that ride's future.
So for rides designed in the era of Splash Mountain and before, if guests are riding the attractions as designed, there's rarely a problem. And there's precedent showing that attempts to correct that can bring more harm than good in an actual emergency.