The only way in taht you can really store your crypto is if you have a hardware waller, or at least, a very good and protected wallet that is almost unhackable because of the high encryption that it has in there.
If you'll consider the situation, there are crypto holders that can't avail to purchase a hardware wallet so that's already mentioned my OP that they can use desktop wallets / mobile wallets.
I will have to disagree with you soon. I seen that Blockbid exchange that is in beta testing is one of the first to be fully covered by cybersecurity insurance.
Still an exchange is an exchange so if its your money and you are good for storing large amount of money there, it's up to you. But the warnings has been spread in the community that don't put much crypto in exchanges that you can't avail to lose.
The warnings that are spread around the community are because most exchanges have no insurance if that exchange was hacked. These warning are correct and should be listened too.
With all the exchanges security against hacking, as well as been fully insured that if it does get hack your coins are returned, then yes when blockbid is up and running it will be way more secure and safe.