It's the "solution" part that is important, i.e., agreeing on the border that satisfies both, solving other claims towards each other, removing the presence of each state from the other state's territory, etc.

Mere "peace" is absolutely not the meaning of the phrase. If it were, the phrase would be unnecessary.

The phrase was dreamt up by Western Israeli allies to promote an oppressive pipe-dream border arrangement that was not even remotely acceptable by any reasonable standards. Only propagandized westerners even speak of it.

This is done so the Western media can frame Palestinians as uncooperative.

What is an alternate solution to the decades-long conflict which is not a "two state solution"?

a democratic state, which can only be achieved if the ruling class wants (they don't) it or the working class demands it.

extending, perhaps, "from the river to the sea"? How do the most fervent of the people who fight for that ideal feel about tolerance, democracy, pluralism, etc?