IIRC, the end of the movie was like a trip through hell, purgatory, heaven etc.
They fused because they are both the same, they are both villains (in Hell) and to borrow a phrase from another movie, "Evil always finds its truest form."
And I want to say that Max had a copy of the doctor's brain which is another reason why they are as one in Hell.
And yes, that could be seen as the doctor's punishment to be trapped inside a gibbet in hell.
You can also see what I think is the crew of the Cygnus below Max and the doctor on the stone bridge.
The religious and metaphysical themes are confirmed on Wikipedia .
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In the novelisation of the book (by Alan Dean Foster)
there's no mention of the ultimate fate of Reinhardt beyond his death
"
Reinhardt’s eyes bulged from sudden, savage decompression as he and the tower were thrown off into space.
From decompression of flesh, from decompression of dream " however we do see the fate of the crew of the Cygnus as they merge consciousnesses to form a gestalt entity
" Kate was Kate;
Charlie, Charlie, and Dan Holland still Dan Holland.
Even Vincent was there.
They were themselves … and yet something strange and new, a galactic sea change that produced all the above and a new unified mindthing that was KateCharlieDanVincent also.
Dimly they/
it perceived the final annihilation of a minuscule agglutination of refined masses—the Palomino.
It was gone, lost in an infinite brightness.
They/
it remained, content and infinite now as the white hole itself "
It's therefore likely that the final vision in the film (of Reinhardt's eyes within Maximillian's exoskeleton) is that they've also joined their consciousnesses to form a single thought-based entity rather than the more literal interpretation of him using Max's outer shell as a makeshift spacesuit.
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As the movie earlier mentions that Reinhardt had murdered Kate's father, and he had used the crew to create his zombie crew, I alway got the idea that he had used Kate's father to create Maximillian, and he eyes
you see inside Max's face were actually those of Kate's Father, as he finally gets his revenge on Reinhardt.
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I just watched it last night.
I think the Hellscape is actually the wreckage of the Cygnus, trapped forever somewhere near the event horizon of the black hole, and Reinhardt merges with Maximillian because the law of physics have broken down in that place.
It's horrible and poetic.
That he's on a "mountaintop" while the demon shards of his crew shamble below suggests he's the eternal ruler of some private corner of hell.
Meanwhile, a white hole seems to open up in the midst of all that, and an angel guides the survivors of the Palomino's crew to a new part of the galaxy.
What is the angel?
Kate's father?
God?
And how will the humans survive without supplies in what might even be an entirely separate universe?
I know it's supposed to be a a "good" ending for them
but I worry for their safety.
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My impression from the end of the film was more that Reinhardt encountered Maximillian beyond the Black Hole, and put himself inside the robotic suit more for the purposes of an environmental suit.
This is why we see Reinhardt's eyes through the visor of Maximillian's helmet.
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The Dr. had asked Kate to protect him from Maximillian earlier in the movie, which I think was because he feared that it would eventually kill him.
However, he wasn't afraid of the black hole which was deadly.
So by merging with it, he was trapped with the object of his fear.
This fate was worse than just death.
His true punishment was becoming the kind of creature that he had turned his crew into...
they were more robot than human.
Now the Dr. is in the same kind of hell that he had trapped his crew into.
This was compounded by the fact that he was trapped inside his own creation and trapped inside his greatest fear.
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At the dreamlike end of  The Black Hole , Reinhardt fuses with the robot Maximillian, appearing to be trapped inside him like a gibbet. What does this mean?
In Disney's "The Black Hole", why do Reinhardt and Maximillian fuse together?
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<the-black-hole>
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It is likely that the final vision in the film (of Reinhardt's eyes within Maximillian's exoskeleton) means that they've also joined their  consciousnesses  to form a single thought-based entity rather than the more literal interpretation of him using Max's outer shell as a makeshift spacesuit. Reinhardt and Maximilian are both evil forces and merge together to join their consciousness to become a single thought-based entity. 
Reinhardt and Maximilian are both evil forces. They merge together to join their consciousness to form a single consciousness and become a single thought-based entity. 