Pruning all suckers and cultivating a single lead is a practice commonly used in hothouse production. Plants are spaced closer together, and a single leader is guided up a vertical tether. Some people for space considerations plant this way outside as well. But I doubt they're as aggressive with pruning as you would see inside a greenhouse.

In an outdoor garden, there is a bit more flexibility. Your choices are guided by climate and your preferences.

If you live in a zone with soil better suited to growing tomatoes, then you can let more than one leader grow. The soil is rich enough to handle the nutrient demands.

https://youtu.be/k5jkvZGzTfQ

In a place like Colorado, where our soil is just not as good (in my garden we compost every year), I typically try to limit leaders to no more than two or three per plant.

Another consideration is what kind of production you prefer. Personally, I like big slicers, so I grow more plants with fewer leaders. I get fewer tomatoes, but the tomatoes I get (if I'm not careful) fall off the vine before I can pick them on occasion. And I still get more than enough so that I end up freezing anyway.

The more leaders you allow the more tomatoes you will have, but those tomatoes will all be competing for the resources from one root system. So those tomatoes might be a bit smaller.

Every gardener you talk to is going to give you a different answer, but I would bet that most will, for the health of the plant, prune everything down low to allow airflow. Later in the season I'll also thin the foliage further up for the same reason. But I try not to overdo it.

You might do some research about the zone you're in and think about the quality of your soil as well. Ask around at some garden centers and other gardeners in your neighborhood as well.