Linux: setuid programs without read permission

The first question that sprang to my mind is Why does sudo have write permission for root?

Broadly, suid programs are pretty dangerous and you should grant them as few privileges as possible. You can't get much more restrictive than only execute permission!

If you can read a file, you can disassemble it. And if you can disassemble it you can look for security flaws and make it that little bit easier to discover attack vectors.

sudo is a little more vulnerable to attack than su as you don't always need to supply a password to have privileged access to some resources (depending on how it's set up). This may warrant tighter security.