If the Fed is already often failing to achieve their target inflation rate, wouldn't raising interest rates cause them to undershoot it even further and lower investment / set off a recession?

I think their point is that while it's arguable that rates are too low, congress needs to change fiscal policy for them to be able to raise rates, so it's unfair for the Fed to get all the blame here. They're using the policy tool they have to execute their mandate and the other (maybe better) policy tools are out of their hands.