"Medieval" isekai: why a horse-driven carriage instead an armored all-terrain vehicle?

and if it was that simple, the world would have it already, in some form.

If all you need is to apply magic then the question is not why does the character not make X, it is why with magic to replace science has the world not made X already. People are curious, and tinker. If they have a magic that moves things already, one of the first things anyone is going to ask is can I use that to make this cart move without a horse, and there would be to many valid reasons for wanting such a device.

Outside of horrible writing, there will almost always be some limitation or reason that vehicles like this do not exist, or are not widespread. Sometimes that reason is a missing piece of knowledge the MC comes over with, but in most cases if it is simple the world will already have it, have had and lost due to some disaster, there will be something blocking the development like a religious ban, or they will show signs of developing towards it already. 

It  would be too conspicuous and the MC would wind up being mobbed and inundated with questions along accusations of black/demonic magic. 

Arifureta has  MC building something like a Hummer iirc. Honestly, that was the only isekai which felt like MC was actually FOR REAL improving carriages, rather than the usual trope of MC stupidly continuing to  enchant or tweak run-of-the-mill horse-drawn ones. 

Imagine riding a carriage being propelled by water jetting out of it's rear!  

BTW, I made this kind of vehicle when I was a kiddo (not that fancy):

(these things are coming back)

No need to know how vehicles work on Earth.  About the motor thing, you are in a world with magic and golens. See what others did and make something like that. I bet it's easier to make a motor that turns Mana into rotating torque than to make a horse golem. 

Because majority of the transported individuals are neets, highschool boys, highschool girls, salaryman & office ladies with little to no knowledge about building modern vehicles. 

Which requires such golems are easy to make in that world, but it they were then the horse and buggy would have already have been replaced with golem vehicles.

The only time you are going to see a MC make modern looking vehicle when everyone else is using while everyone else is using equine and similar beast powered transport, other then horribly writing, is when the MC has some cheat or ability that the rest of the population does not which allows it to be made which the rest do not (like in Arifureta, where the Mc is the only person capable of that level of enchantment) , or they are not used due to being cost prohibitive for some reason (in most D&D settings the cost of making a golem is so high it would not be worth it, and all but the most successful merchants would never be able to afford one anyway). 

A horse-drawn carriage gives more of an old-school feel!