Resizing on the fly has become an essential feature (that bottom right corner), as well as being able to switch from a fullscreen app without having to resort to silly gestures.
The "problem" Apple seemed to be trying to solve with Stage Manager on iPad is that people can lose track of their windows
Perhaps, but you absolutely do not have to use it for that. I can see all my windows just fine in the overview without Stage Manager. It allows for switching between windows faster, especially if you want to switch back and forth relatively often. Sure there are gestures too, but for example swiping left/right to go back and forth between apps you don't visually see what you'll be switching to, and that particular gesture is incredibly unreliable for me (to the point of being useless), and requires a relatively big hand movement.
The bottom right resize corner has the advantage that you can resize blindly (the "hitbox" for it is much bigger than the visual indicator) which works 100% of the time and it allows for a new way to, for example, switch from a fullscreen app to checking your e-mails real quick and back. Whilst still looking at the content you exit fullscreen mode with the corner, so even as you do the motion you can still see the content.
If you were to swipe up from the middle bottom to get the app overview it would require your right hand to move towards the middle of the iPad and then swipe up, blocking view of the content as well and requiring you to lift your right hand if that was holding the iPad on the side (when not docked of course). Instead of ending up in an app overview the resized app's content remains visible.
Depending on how I move the corner, I get only the dock, or I get only the left panel, or I can choose to get both. I can now open Mail from the dock, or from the left. Don't want the dock? You don't have to use it. Only use the dock and tap the icons there to switch between apps and not care about the left side panel? Works fine as well.
Overall this works more reliably for me and reduces the amount of movement with my hand, making it much more efficient than the gesture-based approach. I multi-task heavily with dozens of windows, without Stage Manager that's a miserable experience. Once you have to start scrolling in the app overview all efficiency has gone out the window anyways, I don't wanna scroll to find an app like I'm on a smartphone with a 6" display.