Many years ago, there was primarily telephone (or telegraph before that) and U.S. Postal service for communication at a distance. Now we have the Internet with email and social media hubs, texting, etc. There was no way to ensure communications with and between governmental figures were even identified as such, let alone preserved. And, of course, it was only recently that some types of communication, such as emails, were required to be kept separate from personal communications and preserved in the public record.
I am all in favor of keeping governmental communications separate from the personal. Mixing the two can only make preservation more difficult. I see no way, however, to guarantee there will never be an email that should have gone through official channels from sliding through in another manner. And there will always be some overlap, since congratulating someone on the new baby could end up on a government account just as well as the congratulation could come on a personal account where the missive adds, “See you at the next Cabinet meeting, and bring that info I asked you about.” It will likely still happen.
Indiscriminately raiding personal accounts of government officials is not the answer, unless the answer is to guarantee no one will ever want to serve in the government. Try to make the law clear on what must be limited to official accounts and leave it at that. When violations occur, deal with them.