This tendency is evidenced by both practical experience and academic research. By shielding monetary policy decisions from political interference, price stability can be maintained without having to give up economic growth. Indeed, in that sense having an independent central bank is a good thing for all concerned.
The reason for central bank independence is that monetary policymaking under the influence of politicians tends to focus too much on short-term considerations. This can easily lead to temporary, non-sustainable increases in growth, but inevitably results in lasting increases in inflation with no lasting gains in growth and employment at all.