Suppose I want to identify the perpetrator (call them X) of some suspicious/illegal activity online, with the help of the authorities.
X uses some legit, short-memoried VPN. But X uses some standard browser like Chrome to connect (through their home router!) to that VPN.
Now suppose I find out about some browsing history of X. Google (or Mozilla, Microsoft, depending on X's browser) sure has a record X's browsing activity, so if they collaborate with the authorities, they could probably pinpoint my identity just out of that browsing history.
Once I get the domestic IP of X, it should be enough for the authorities to identify them.
Am I right? VPNs may preserve privacy but X can always be traced provided they connected to the internet through their home router.