Try it, and your questions about why making the window any smaller would be affirmatively bad will go away.
Red-dots offer a significant performance advantage for handgun shooters who learn how to use them, particularly for high-speed shooting. Significant. But the big challenge is that, when the dot is out of the window, you have only your index/kinesthetic sense to find it. So having the dot in the window over the widest range of view angles is very, very important.
Let's say you draw an iron-sighted gun. Let's say you miss your draw just enough that the sights aren't perfectly aligned when you get the gun up to the target. Your eyes will notice where the front sight is (or, if it's grossly low, that it is missing); you will know immediately which direction to pitch or yaw the gun to get the front sight into the notch.
Now do the same thing with the red-dot. If the dot is not exactly centered, but still in the window, no problem, you still have the same amount as corrective information as before, and can "fix it" very fast. But if the dot is not in the window, you have no visual information from the sights to tell you which way to pitch or yaw the gun... you have no visual information to tell you whether the dot is above the window, below the window, left, right, etc.
This is why it is very common for shooters who are new to using red-dots under time pressures (in a shooting match, timer-involved practice, a class, etc.) to draw lots of figure-8's in the air as they frantically "hunt for the dot" after they miss their draw. This is NOT GOOD.
The larger the window, the wider the range of not-perfect presentations will still let you see the dot, even if not centered. The smaller the window, the greater the likelihood of losing the dot.
This same dynamic presents itself in miniature after every shot. As the gun oscilates in recoil, the dot will move up (or sometimes diagonally up depending on the user and the gun), leave the window during the full extent of muzzle-flip, then move downward again as the slide closes and the gun recovers from recoil. If things are going well, and the gun and ammo and shooter are all well-tuned, the dot will return on its own to the same position. If the slide closes relatively hard, the dot may travel back through the window and then dip below, and then bob back up again.
While the dot is out of the window, you have no visual information to use for where the bullet would go if you pulled the trigger at that instant. You have to wait for the dot to re-appear - and your brain also has to process the dot's appearance and location, which is not instantaneous, though it is very fast. The larger the window, the greater the fraction of time during recoil the dot is visible.
The more time you can see the dot, the faster you can shoot. Really proficient shooters shooting fast "shoot the streak," firing as the dot, still in motion, moves through the acceptable target area. It's easier to shoot fast with dots than to shoot with irons BUT ONLY WHEN YOU CAN SEE THE DOT.
A smaller window would be BAD, not good. The gun would shoot worse.
Here's a video showing a shooter's-eye view in slow-motion of how the dot moves on a purpose-built competition pistol with a big window (same type of sight I pictured above).