This isn't the correct forum to discuss firearm technology, but since you asked the question I'll expand a little bit more.
To understand the place of safeties on firearms it helps to begin by thinking about how they are typically carried. Shotguns and rifles are typically carried loaded and slung over the shoulder on a strap. Handguns are typically carried loaded and in a holster.
External safeties are extremely important when carrying a loaded shotgun or rifle because the trigger could easily be pulled if caught by an errant twig, if stepped on by your hunting dog, if the person trips and falls onto rocks, etc. The purpose of the safety in these cases is to prevent the trigger from being pulled in these sorts of accidents. External safeties have been a common feature on shotguns and rifles for over a century.
Handguns are historically carried in holsters - the holster itself is the first line of protection from the trigger being "accidentally" pulled in a fall or by something external like a tree branch. Typically the handguns is ready to fire as soon as it is pulled from the holster.
There are exceptions - some handguns do have external safeties as I'll now explain.
Revolvers: Pretty much universally do not have an external safety. The few that do are historical anomalies.
Pistols: Some do have safeties but most do not. The best explanation I have for this is that there is not universal agreement among police and military users as to whether safeties are a good feature or not. Some police forces specify pistols with safeties because they want their officers to be very deliberate before potentially shooting someone, most police forces reject safeties because they are afraid in time of stress the officer might forget to turn it off - and get killed due to the delay.
I don't have sales figures but I would bet that 8 out of 10 modern handguns sold today do not have external safeties.
Edit: Specifically regarding your question about carrying a handgun inside your pants with no safety: It is practically impossible for a modern handgun with a properly designed internal safety (*1) to fire unless the trigger is pulled (*2). There is no legitimate fear of the gun "going off" although the acts of holstering and unholstering are dangerous if the trigger finger slips onto the trigger accidentally.
(*1) = I do not claim that all handguns have a properly designed internal safety, some of them are junk.
(*2) = Technically the gun can still fire if it reaches a temperature of about 300 degrees. If your pants are at 300 degrees you probably have other things you are worrying about.
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