Page file is not a cache. It stores data of running applications / processes that do not fit into RAM. But when you turn off or restart PC no applications are running, so all data in the page file are not used anymore. There is no running process that would own them and use them.
I assume you have SSD. Writing to SSD is quite complex, because of limited lifetime of SSDs. So there is some “cleaning” needed sometime. And possibly cleaning page file also triggers some “cleaning” of SSD and that results in better SSD performance for certain time.
And possibly better IO operations lead to less CTDs. I posted another thread about my observation.
Btw, cleaning page file is done for security reasons. When an application / process ends, the data in page file owned by the process are not owned by anyone and thus not used. But they are not cleaned until some other process overwrites it. And now imagine you opened confidential document and part of it is stored in page file. You turn off your PC, but data are still stored in the page file because cleaning it takes lot of time. And now someone steal your PC. He cannot read the document, because it is hopefully encrypted as it is confidential. But he can look into page file and find pieces of document there.