> And bonds require, at minimum, two electrons shared between the two atoms. That's why H2 is pretty stable compared to monatomic H1. You'd have to rip up and throw out hundreds of years of chemistry for H4 to be possible.

Actually, all you have to do is catch up with (checks Wikipedia) 100-year old research. Molecular orbital theory is needed to understand three-center two-electron bonds, and that dates back to the 1920s. However, the concept of "a bond is an electron pair" only predates that discovery by about a decade. It actually turns out that H₃⁺, the classic example of the three-center two-electron bond, predates both of those discoveries.

It's also worth noting that chemistry itself as a recognizable field only dates back to maybe the 1760s, and things like bond structure only really start to be worked on in the mid-19th century, with most of our modern understanding dating from various parts in the 20th century. So that's hardly "hundreds of years of chemistry" that would need to be ripped up and thrown out.

Let me guess, you never took any chemistry classes past gen chem in college? Molecular orbital theory and two-center three-electron bonds is bog standard organic chemistry (might even be first semester orgo, I'm not sure).