There are three problems with that approach.
1. A proper trigger wheel will have an extra or a missing tooth to provide an absolute reference. The computer will know that this indicates a given engine position. When you start the motor it will start to see pulses but as the computer doesn't know where the engine started, it won't have any position to start counting from. Once it see's the extra/missing tooth representing a given angle it can then keep track of position. If the extra tooth was at 0 degrees and you had 60+1 teeth on the wheel(6 degrees per tooth), the computer would know that at 0 degrees plus 3 teeth you'd be at 18 degrees. 0 degrees plus 11 teeth would be 66 degrees...
Let's say we weld the distributor shaft as you suggested and timed the motor at TDC. Each time a pulse came in to the computer, it would know the position was 0 degrees, 180 degrees, 360 degrees or 540 degrees(720 degrees per 4 stroke cycle) but would have no way to determine which.
2. Assuming the issue above is solved, and there are ways to solve it, the pertronix would be capable of providing an accurate indication of position every 180 degrees. The problem is that these position indicators are so far apart that the engine could change speed enough to throw off the position calculations.
Let me use an anology to help explain.
Let's say I told you the time once a minute and I asked you to tell me when it was 37 seconds past the minute, only counting in your head. Chances are, you'd be off by at least a few seconds or more. If instead I told you the time every 5 seconds, you'd be able to tell me when it was 37 seconds past the minute with very little error. Likely less than a second off.
In the analogy the error is due to variations in your counting between the last time I told you the time and the desired time. In the ignition system the error is due to changes in engine speed and changes in acceleration that happen between the last tooth and the derired engine position. The errors are in different places, but have the same affect...
3. Electromotive requires the use of a given wheel configuration. It will fall on it's face without it....