I like smaller size wheels and tires because they are more affordable, and easier to peddle on a bike, or use less gas on a car because smaller wheels and tires don't weigh as much as a very big wheel and tire on a bike or car.
I also feel having a bigger tires increases the chance of a sharp object like a nail on the road damaging a tire when a large wheel rolls over a nail. But, a smaller tire has less rubber which touch the road, so there is less of a chance of a small object like a nail breaking a tire on a bike or car.
Smaller wheels and tires are also less likely to get stolen because smaller wheels and tires are usually worth less money.
A smaller wheel and tire has a cute and unique look on some bicycles like smaller bicycles and smaller cars like the original VW bug, older Mini Cooper from the Mr. bean TV shows, and Smart cars.
Smaller tires are more affordable. I'm lucky to have a smaller car that don't need very big tires to begin with so they are that expensive when compared to other vehicles. On my bike, I've always had a mountain bike with bigger tires. I can go off the road and ride my bike over rougher terrain that way though.
I also prefer bikes with smaller wheels. I think it is easier to peddle fast enough to not tip over.
I seen some videos and photos of people riding very tall bikes. I feel it can be more easier to fall off, or run into people by accident. Those giant bicycle wheels are most likely hard to find at most bicycle stores, and cost more.
I have average size tires for both my car and truck. My truck uses 265/70/R17s which are not an overly large tire in comparison. There are truck tires which go up to 33" (mine are 17s). But those require a lift kit to work.
As for why one might want larger tires, there are a few reasons. Increased width of the tire means more contact with the ground. This creates a more stable platform and means the vehicle is less prone to tipping. (It's why larger truck tires are wider.) Plus it disperses the weight more effectively and thus means less force exerted on the asphalt. (Higher pressures on asphalts mean more likely to cause damage to it/the tire if something happens.)
Plus it gives more room in adverse conditions, like high water, to move water out of the way and prevent hydroplaning.
Conversely though too much contact makes the handling harder as it has to move more material. But like all things there is a tradeoff.
Taller tires also tend to perform better in winter conditions (moreso if they have an aggressive tread) since they have more tread before they get clogged with snow/ice and travel further to help remove anything stuck in tread.
Those who go into the woods a lot tend to prefer larger tires because they sit the vehicle up higher and clear obstacles easier.
Also the amount of fuel difference used by large vs small tires is very minimal. I mean the weight difference between them is so tiny it's basically inconsequential. (The tires would be less than adding another person into the car/truck. And fuel economy between a car with 1 person and 2 people doesn't change enough to notice.)
It's far more likely to be affected by driving habits or whether the tire is properly inflated. By that I mean someone who floors it at each red light will burn more (regardless of tire size) than someone who accelerates slowly even if they have the exact same vehicle.
In terms of cost, smaller tires can cost less... but that's no guarantees. There are tires for cars that cost over a thousand per tire. (These are the high performance/high speed tires oft used for sports cars or expensive cars.) Similarly truck tires can get pricey too. (My truck tires cost $250+ per tire... ) All depends on whether you're buying a solid name brand or some discount rubber. (I recommend always buying a name brand just because for tires you do get what you pay for. And, bluntly, your life often depends on it. )
That is a good idea to stick to the recommended tires unless the tires which are recommended have bad user review. I think it is a good idea to be careful on who you get your recommendation from since some car dealers or car brands may recommend tires which are overly expensive, and not needed for average road cars. They may also recommend tires which are not as good as alternative tires which dedicated tire shops recommend for a person's brand and model of car.
I read a few forum posts online of people having to pay more money for tires at a car dealership garages where there is less choices in tires, and the tires sometimes don't last as long as a higher quality tires which is sold at a dedicated tire store.
Some of the less honest car dealerships may sell lower quality tires to make you come back every few months to years for tire repairs and new tires because the tires you bought is unrepairable because they break apart more easily than a higher quality brand, and also want you to hire them to do car maintenance and repairs which you don't need or is more expensive than other car repair shops.
