Interesting mind game.
However, the reality is that the faults and double faults won't occur symetrically. Look at the 50% scenario again. While satisfying that 25% or 1 in 4, rate of failure, randomness dictates the double faults will not be spaced evenly. It won't be 1-2-3-miss, 1-2-3-miss, etc.. Randomness states that those misses may come together in pairs or bunches. How about at 15-30.
This discussion involves reversed reasoning. Its like getting lost in follow throughs to the point of distraction and losing sight that a proper follow through is a RESULT of the proper balance and mechanics that precede it. You can also perform everything incorrectly and artificially force a proper follow through. But to what end?
Serve percentages are a RESULT and are success/failure indicators to be analyzed in the post mortem of a match. The backward reasoning of using a mathematical formula to take what are, in reality, poor serve percentages and somehow transform them into some kind of successful number is frankly, unsound. Like turning iron into gold or like something a snake oil salesman might peddle. The expression "you're only as good as you're second serve" means that you need a strong and reliable second serve that you make near all the time and is effective enough to keep you at least neutral in the point. One shouldn't depend on the law of probability nor a coin flip to decide outcomes on the court.
If this thread is intended as an intellectual exercise, enjoy. But, anyone flirting with this "idea" as a viable approach to play would be better served signing off, shutting down, grabbing a hopper of balls and getting to the job of adding spin to their serves via racquet head speed.
Make your second serves strong through practice of sound technique and you'll never look back.
First rule of tennis....hold serve.