What prevents a person from having access to the wallet?
Math.
The sheer size of the numbers we are dealing with here are incomprehensible. You are wondering about a single person or a single machine generating millions of seed phrases a second. Let's take that to the extreme. Let's say every single one of the 8 billion people in the entire world are generating and checking a billion seed phrases a second, and they all keep doing that for the next 1 million years. In that entire time, the entirety of the human race will have checked approximately 0.00000074% of all possible 12 word seed phrases.
So feel free to set up your computer to generate as many seed phrases as possible from now until the day you die. You will generate billions or even trillions of empty seed phrases, which will be akin to a single grain of sand from all the beaches on the planet.