You might as well have a car with two steering wheels each controlled by a different person.
Of course, given excess fiscal stimulus, the central bank can negate the excess by raising interest rates (or make up for inadequate fiscal stimulus by cutting interest rates). But there’s a problem there, as follows.
There must be some optimum rate of interest, and assuming that before the above excess/deficient fiscal stimulus is implemented that interest rates were optimum, then AFTER implementing the excess/deficient fiscal stimulus, interest rates must be non-optimum!!
The latter “monetary policy fighting against fiscal policy” is closely analogous to using the brake on a car to control the car’s speed when for some reason the accelerator is being permanently depressed too far: it’s much better to depress the accelerator by an OPTIMUM amount in the first place. (Janet Yellen recently lambasted Congress for not applying the right amount of fiscal policy.)
The solution to the above problem, as advocated by Positive Money is to bar politicians (who are 100% economically illiterate) from taking decisions on stimulus, and have economists (who are on average slightly less than 100% economically illiterate) take the decision.
And that is easily done AT THE SAME TIME AS leaving purely POLITICAL decisions in the hands of the electorate and politicians.