I don't understand your logic, but you seem to have it the wrong way around. If you want interest rates to be higher then we need to restore the economy to healthy growth first. We can't restore the economy to healthy growth by raising interest rates.
Interest rates are just the price of money. Like any price, their purpose is to balance demand and supply. It makes no more sense to say the interest rate should be at some arbitrary level than it would to say the price of apples should be kept at some level even if there was a glut of apples. The only 'natural' rate of interest is the one that would balance the economy at non-inflationary full employment.
https://en.wikipedia.org/wiki/Natural_rate_of_interest
If you want interest rates to be higher to encourage saving you should actually be in favour of more government borrowing because that is the only feasible alternative. Otherwise we have the problem illustrated by Keynes'.
https://en.wikipedia.org/wiki/Paradox_of_thrift If everyone tries to save more at the same time the result will be counterproductive because the impact on the economy causes incomes to fall. Somebody (ie government) needs to spend more to avoid this outcome.