Because in reality the two party system is not accurate. It’s rich versus poor, those with power versus those without. Nobility versus peasants. That’s just how it works.
The US federal government is already pretty weak compared to other countries. The federal government looks pretty bad at the moment, but I’m not sure further weakening it will help the country.
The US federal government is very strong compared to many countries, just limited in where that power can be applied... in theory. In practice, the insanity that is a precedent-based judicial system over time means that it's all just a disorganized mess where on one hand the Feds can straight up prevent you from boarding a plane, ever, without any semblance of due process (this is not normally a power you'll find in other countries), and yet can't regulate many mundane things like firearms.
However, there is a very solid case for a weak federal government, and it is simply that US is a country that's way too big for any coherent national policy on most matters that we've currently pushed there. It's such a vicious fight because it's half the country trying to bludgeon the other half into submission, motivated by the knowledge that, if you yield, the other guy will pick up this huge club and do the same to you. This will continue until the country breaks down unless we dial it down to state level and accept the fact that other states may have laws and lifestyle that is despicable or horrifying to us in some ways. Either that, or we might as well just break the whole thing apart now and not wait for it to happen in a more violent manner.
Other countries don't institutionalize the two-party system by law. Because it would be insane and antidemocratic to create a complicated network of laws that would have to be eliminated state by state in order to ordain that an entire country must be ruled by two intimately-linked private clubs in turn.
The two-party system isn't so heavily institutionalized "by law". The law generally gives advantages to parties that pull in more than x% of the vote, and it so happens that the first-past-the-post system of electing representatives makes it very difficult for a third party to take root.
Except our law is nothing like that. You can have a party take 45% of each district across the whole country and end up with zero seats in the House (because the other party took 55% of each).
The first past the post system is encoding a two party system into law. If it makes to hard enough for a third party to take hold, there might as well not be one.
A big step forward for the USA would be a vast reduction of federal power over the states.