So I noticed something very interesting about Vox and his victims.
After killing 1st victim:
After killing 2nd victim:
Everytime Vox killed in his past he completly copied his victims behaviour, talent and even their style. And while he sabotaged some of them, he also manipulated the others to trust him. He pretended to admire them or help them out only to betray and murder them.
And we as the fandom lots of time pointed out how similar Vox behaved and dressed as Alastor:
So my guess is knowing how Vox behaved in life that Alastor might have been his perfect victim type. He already started to take on his style but unlike his other victims Alastor didnt fall for his tricks and saw right through him and he couldnt even hurt him.
Because of these he was never able to get over his obsession and switch to a new person.
I am not saying that in a first time ever Vox didnt genuinely wanted to be partners with Alastor or saw him as his equal but I also think his messed up serial killer brain might also has something to do with wanting to be with Alastor.
And if Alastor knows about Vox past and behaviour it is easy to see why he laughed at him and denied their partnership. He thought he will be Vox next victim. Used and discarded as nothing. He probably couldnt believe that Vox would try to manipulate him too.