[Serious] It seems like it’s common advice to not leave crypto on an exchange and keep it in a cold wallet. Doesn’t that create a whole other set of insecurities?

I understand the risk of keeping crypto on the exchanges, as many have collapsed before and many will continue to collapse. But is it really safer to keep it in a cold storage? If I have a serious amount of crypto (say $1,000,000+), setting aside the inflation protection, isn't this the equivalent of keeping a giant stack of cash or gold under the mattress or buried in the back yard? Conventional wisdom is only crazy people do that. Somebody could come physically steal it, the hard drives or backups could be corrupted, you could lose the password, the house could burn down, etc. With a serious amount of value, it seems really really risky to me, but I'm not sure what a "safe" alternative could be.