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DanielLC comments on A Proof of Occam's Razor - Less Wrong
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Your proof can't be right because it doesn't use the concept of "complexity" in any non-trivial manner. If we replace "complexity" with "flubbity", so that there's only a finite number of hypotheses for any given "flubbity", your proof will still go through.
For some actual work on justifying Occam's Razor, see Kevin T. Kelly's Ockham Efficiency results. Kelly unpacks "complexity" in a nontrivial way that isn't just description length.
ETA: see this earlier discussion about learning and simplicity, it's very relevant to the topic of your interest.
Interestingly, flubbity will correlate with complexity, regardless of how you define it. This is for pretty much the same reason as the inverse correlation of complexity and probability.