I've kept my money at a major bank since I was a teenager and they were never shut down by the government, and their database never lost my account information. I guess I trust it.
I'd argue that their value has diminished, akin to a scenario where some of them are lost, much like a bank losing a portion of its deposits.
Put it another way, Haypenny currencies are like Bitcoin but without mixers (and you need a valid court ordered subpoena to look at somebody's private transactions vs. with Bitcoin any criminal with a web browser can do it).
You haven't persuaded me yet about the potential outcome if your government mandates KYC collection or imposes closure, a scenario highly likely in today's world.