IMHO Even thought the provider would log it is still better than not using one in a lot of cases. If whoever can see my VPN address, he would otherwise see my real address directly.
In that way he has to find a way to get the VPN provider to give out my real address. What might be possible with a lot, but for sure not with all of them.
Also think countries, my country does barely have any contracts with other countries for crimes like this. So they would have to use a complicated way to actually force them to give out my data.
In most situations we are already way over the realistic damage done in forms of costs to catch the individual.