its a fairly niche thing, mostly used for fighting games.

most fighting games are, at least to some extend, based on streetfighter 2, a game that released on arcade hardware, before analogue sticks were a thing.
so most fighting games can be played just fine without analogue sticks.

most enthusiasts played on arcade style controllers, where the stick works more like a dpad on modern controllers.
but some players started switching from sticks to a 4 directional button "leverles" setup.
some say that it is more ergonomic or more precise.

there is a learning curve to using it, but that is imo verry dependent on what controller you used before, and how you think about it.

Leverless controllers are fairly popular. Supposedly more ergonomic and precise than an arcade stick or pad controller, more portable than the stick, and better to use than a keyboard.

It is a fairly large learning curve if you've already played fighting games with another input method, but after building some new muscle memory, you'll realize that your understanding of the game is still intact. There are also some really good "shortcuts" in input methods to get precise, just-frame inputs, allowing you to input opposite directions just 1 frame apart, with no stick travel time.