Well, you've a "terrible flaw" here:
Shareholders of company A start selling their stock to buy from company B
If BTC has double the price then, unless company A still produces 50 BTC anyway, its shares will be down to 0.5. So investors in A wouldn't gain anything on the rally over B, and most likely would loose a lot, as within the selling rally the price would keep dropping at a fast pace.
You do realize that the outcome of company A's share price is the same right? You are confirming my conclusion.