I stand corrected. The safaris that my friends have all gone on, the guides all had guns. But perhaps they all went on different types of safaris.
One of our guides in Botswana deliberately provoked a young male, who like to practice their combat skills. He kept easing forward toward a group, basically using the truck to act like an aggressive animal. One of the young tuskers charged, trumpeting and ears flapping and kicking a ton of dust into the air. The guide quickly slammed the Rover into reverse and roared off. Scared us, but he was laughing, and explained that it was a mock charge and how you can tell a mock charge from a real charge because of all the fanfare (ears, trumpet, dust). He said a real charge is pretty much silent, trunk down and ears back.
We went on one night drive, but it was so nerve-wracking, one was enough. As the truck moved along the trail, a pride of lions fell in with us, having learned that bright headlights and a spotlight with several million candlepower is perfect for locating prey.
We went on safaris in Botswana, Tanzania and Uganda and never saw a guide with a weapon, although I think they may have had one in the camp to use for those who wanted to go on a walking safari.
The term “safari” covers a lot of ground, from taking a drive in the backwoods with a pair of binoculars hoping to see something to scheduled organized tours in small, well stocked parks. I don’t think you can generalize. The guides on more formal safaris I’ve been on have had guns in cases the vehicle. The safaris in remote and undeveloped parks offer everything from “a large stick” to “lessons on how to run away.”
A while back one of my good friends did a tour through various African countries as a travel writer. He went to a game park and they were given the option of sleeping in the ranch building or putting up a tent right outside. Thinking this would be fun he and another fellow put up their tent and settled in for the night.
They didn’t realize until later that they were the only ones who stayed outside - even the guides stayed indoors.
Late at night my friend woke up because he could hear large animals moving around. He looked out the mesh and saw two lions. He very quietly woke up his tentmate and then had to talk the guy out of “making a run for it” to the main building. He zipped up the tent (so the lions couldn’t see in, he said they told visitors that as long as they can’t see in, a tent is just another big object like a rock as far as a lion is concerned) and then the two of them crouched there, wide awake and scared as hell, staying still and quiet for hours. At some point one of the lions decided to lie down against the tent for a snooze. I don’t think my friend has been that scared before or since - he had to take a leak and his legs were cramping but he was too scared to move.
Morning came and the lions wandered off and my friend has quite the story to tell 
Nothing is as dangerous as a virtually-materialised elephant, IME.
Do they tell him some rich wanker is going to be shooting at him ?
It’s amazing (and scary) how quietly and unobtrusively such a large animal can move through dense forest. You would think they would make a racket but they barely make a sound. One minute the roadside was empty; I turned around for a second and when I turned back after my assistant whispered a warning there was a 3-ton animal staring at me a few dozen feet away.
TV execs prick their ears and mull over the concept of a new series: Columbo: Safari Detective.
I went on a river safari in Zambia, and my guide (who was simply amazing, and knew the river and the animals up and down…you couldn’t ask for a more knowledgable professional) had a similar tale. He had been guiding a night time fishing trip when he heard lions approaching the camp. He quickly got everyone in the tents, which are considered safe as long as they are opaque. Unfortunately, it was a full moon and a lion noticed him as he scambled in to his tent. The lion stared menacingly, and the guide grabbed the only possible weapon-- a tent stake, and held it to his heart, hoping to at least injure the lion when it attacked. The lion crouched and began to prepare to pounce. THen, he let out a roar, stood up full height, walked over to the tent…
and peed on it. With his business done, he walked away.
Thankfully for us, the guide waited until the last night of the open-camp safari to tell us that story!
Sometimes the kitties get pretty close. The cheetah didn’t really seem to pay the humans much mind. I would so want to pet that fluffy head…
What a great encounter. Must have scared the crap out of them when it jumped on the truck rather than appear out the other side. We had a huge male lion appear out of the bush, walking straight at the vehicle. If you’ve ever seen a lion head on, the eyes burn a hole right through you. We were sitting in the back seat of the open truck and the cat sauntered toward us as we remained perfectly still. He disappeared behind us and I seriously tried to make my eyeballs roll to the back of my head to see where he was, then to the left, hoping to see him reappear. It seemed like it took forever, but he eventually appeared in my peripheral vision. I was sure we were about to be dragged out of the truck and turned into chew toys.
You would think you would be safe on top of your own elephant.
That’s why they made howdah pistols. 
The OP is working from a false premise - people on safari do get attacked.
Why don’t they get attacked more often? Because lions and other African predators are not stupid and have been living with humans for a lot longer than, say, grizzlies. They have learned that humans are not always a good prey species. And cars aren’t very tasty. Even worse than tofudebeests.
Plus, I suppose that the animals are scared of humans. Most animals are, they know these humans can kill frlm a distance, never tire, attack in packs and are bloody relentless. I thought that animals who tend to attack unprovoked are those like tigers and bears, who don’t ordinarily interact with humans, like lions or cheetahs.
African predators are very accustomed to giving up ground to species more dmagerous or at least very risky. Elephants, water buffalo, natives etx. Grizzy bears and ploar bears have not evolved around physicaly superior species.
Some years ago, my brother took part in a safari in Namibia; basic method of which was, the guests not travelling in motor vehicles, but riding horses. I gather that such “horse safaris” are quite widespread, at least in southern Africa – horses can get to some places where motor vehicles can’t, and tend to cause less disturbance / increase chances of getting closer to the game.
Instructions to the participants were: if you’re near one or more lions which seem to be getting interested in you as potential prey – get your horse moving and gallop away, at once – a galloping horse is a lot faster than a lion. Just don’t fall off ! I gather that this was an “at your own risk” set-up, with patrons signing well-attested forms to that effect: attempted lawsuits by a fallen-off lion victim’s relatives / heirs, would have got short shrift.
Is that short for “howdahfuk do I reload this thing?! Need answer fast!”?
Shut up or you’ll get us both fired!
Mods: that is an old joke, not an insult.
I think that after several thousand years that perhaps animals with large brains might have evolved the ability to quickly learn from social cues of their parent animals that humans are the deadliest critters they can see if provoked.