Question: What biological factors prevent organisms from continuously fusing with one another? Is it possible even hypothetically for it to work?
It's possible hypothetically to work. Note the emphasis. A lot of things are theoretically possible, it's just that reality prefers efficiency, and this is not efficiency. Not anywhere close.
Also, just to clarify - this isn't evolution. Nothing close to it. Evolution is based off of reproduction, mutation, and changes. This is a single species which can take on multiple forms based on various growth rates, so something more akin to a species of fungus. I mean, somewhat akin to it. But you run into a problem very fast - specialization vs generalization.
In order for any living organism to survive, it needs to do a lot of things in order to survive as a species - get energy, defend itself, reproduce, etc. Now, a smaller organism has to be able to do everything - bacteria has one cell to get energy, defend itself, and reproduce. However, once you start getting bigger, you can start specializing, and specializing is awesome - human muscle cells can't digest complex molecules like the stomach can, they can't defend themselves like white blood cells against foreign invaders, they can't detoxify blood, etc. etc. - but what they can do is they can contract, and they can contract really, really well. An adult human is built up of cells that can't survive without all the other cells.
Let's take your 'fusion' creatures. They can survive on their own, presumably, which means that each creature is capable of doing everything they need to do. When they fuse, that means you're introducing redundancies everywhere. Imagine a pack of tiny humans stacking themselves up to resemble a crude adult human. This just isn't going to work - the 'arms' aren't going to be as strong as a normal humans because it's made up of tiny humans. The bones will be weaker, because it's not a single strong bone, it's a matrix of little fragile ones. It's just not going to end well.
Let's say that these things can do the incredible and reassemble themselves at the cellular level so when they fuse they can shift around the cells. Will that help? Well, no. Because that's not possible. You can't just move around cells with no consequences - if a human decided to move their lungs around, they would die, because they are missing their lungs. It's a colossal amount of energy besides, and there's no blueprint for the end result, and their are a lot more bad end results than there are good ones.
That said, it is a lot more possible on a small scale level and with very simple creatures - nothing more complex than, say, a sponge of jellyfish. Once again, it's not a very good method of creating a creature and runs into problems, but it's possible at that point.