If you mean bowling shoe vs non-bowling shoe (as opposed to exact brand/type of bowling shoe), then they matter a lot even for a complete beginner. In a normal throw you're going to have a bit of momentum moving up to the lane and then release. You need to slide on your feet when you do this. In this [1] video go frame by frame at 12 seconds (or any time he bowls), you'll see his left foot in particular slide several inches during his throw. It's more subtle, but there's also a significant slide with his right foot as it goes across.

If you did this in tennis shoes, or any shoe with proper soles, the friction would cause your feet to stick and it'd be simply impossible. Socks would be much better than normal shoes, but then you have the opposite problem of too little friction and it's difficult to maintain control. Bowling shoes aren't like running or something where a pro runner is going to have some absurdly expensive pro shoe that improves his time by a fraction of a percent. They're much closer to something like ice skates for ice skating.

And yeah that's a pro with perfect perform, but even a beginner who's not just walking up to the lane, stopping, and throwing, is going to have to deal with sliding. It's just part of the game.

[1] - https://youtu.be/_qh4yOwCgOg?t=12

> to get good enough that choice of shoe matters

Bowling shoe vs running shoe? As soon as you’re trying to get better, the shoes matter a lot. They let you use the established techniques.

Bowling shoe vs socks? Never tried it, but I’m going to guess once you can break 100 that socks don’t cut it.

Socks with no shoes are good enough for amateurs. Maybe even better than the worst bowling shoes. I'm not sure where the level of shoes matters is crossed, but socks gets that a lot farther than street shoes.