Trains move with steel wheels on steel rails, which is incredibly efficient, and allows trains 2+ miles long and 20,000 tons*. But steel-on-steel traction is quite poor, and it takes a long time to set brakes on a 2-mile train**. So a train can take a mile or more to stop, and can't appreciably slow down in the ~1/4 mile it might have to see you and react.*** But even slow trains are deadly.****
So it's all on the highway vehicle to make sure it's not in the wrong place at the wrong time. *****
To avoid mass casualty, it's especially important for buses. This ritual of "stop, look, listen" also puts them on guard against other mistakes - like pulling onto the crossing when there isn't room in front of them to fully clear the crossing.
Why does the bus get this extra task when ordinary cars do not? Because of the potential level of catastrophe (fuel trucks have to do the same thing). The fate befalling many people (it usually turns into a national-scale tragedy), and the the ease of making a mistake and leaving the back of the bus still fouling the tracks. (less likely in a car.) Also the impracticality of evacuating a bus.
As far as big special loads, crossings don't have phones like in the UK. They have "ENS" signs with a phone number. It's for emergencies, but if someone is scouting a special truck move, they will simply call that number and make arrangements.
* in North America, Russia, Australia, and other places with the infrastructure for trains that big. 40% of American freight moves this way... Especially in L.A., where almost everything unloaded at the ports of Los Angeles and Long Beach goes onward by rail.
** A lot is done to make air-brake commands move down the train quickly, but it can't go any faster than the speed of sound, can it? :)
*** Due to physics (energy being proportional to velocity squared), in 1/4 of its stopping distance, it won't even slow down 25%.
**** Looking at several years of accident reports, in fatal accidents of people getting in the way of trains (in vehicles or not), in half of all cases the train was moving slower than 5 mph.
***** This can be a culture shock for highway vehicle drivers, where so much of the driver experience is nerfed for your safety: air bags, crumple zones, guard rails, medians, energy absorbing bollards, traffic calming, curve and sightline engineering... trains have not been nerfed.