Why are there no Linux desktop distributions that allow you to not use a password?

Because Linux inherited a lot from Unix and Unix, a multi-user system, developed a sophisticated password/security system after it got the first viruses. Yes this is another use a password answer but it's worth touching on another issue or two. For example an old geek joke goes "if you surf the net as root you may as well be using Windoze". In fact Microsoft has improved somewhat but *nix (Unix and GNU/Linux) is right to prefer to run programs in user, not administrative, space and Windows insistence on the opposite over the years even for computers on the Internet (which shouldn't) helped the multi-billion dollar malware industry bootstrap itself into the monstrosity it is.

Use a password. If your distro doesn't have sudo for administrative work, get it or try "su -c". This IS common sense stuff.

You can indeed setup your accounts to not use a password. It's a bad idea, very bad idea, but there is nothing stopping you from doing so. There are many thousands of hackers out there that would be very happy if you would set up your accounts to not use a password.

Because security is a basic principal of Linux. Only root user has ultimate privileges and that has to be confirmed each time you want to exercise those rights. The reason there are so many viruses for Windows is because such things weren't secured.

I have installed Linux with no password many times, on embedded systems. I am sure with a little tinkering you can get any serious distribution (not Ubuntu) booting into a non root account without a password.

Your DVR runs Linux and it never boots up with password prompt.

There are. But it seems totally useless and stupid to use a very secure system and then dump a lot of the security by not using a password. A would-be hacker using a hacking script could place a hidden program into your user folders. It could be used to spam emails from your machine as an ordinary user is not prevented form doing so. It could also be used to monitor any attempt to sudo (especailly if you use the dangerous no password option, it could even initiate a sudo command) or just to su to root. It could then attach itself to your commands as root. That would give it FULL access to the system including the secure shell. At that stage you would be open to keyloggers and worse. If you want to be that insecure go back to using Windows.