Why don't we hack core?

Question

I couldn't believe that this question hasn't already been answered on this site, but I didn't find it when I searched, so...

Why is it such a bad idea crime against nature to hack core?

• Is it really that great to be able to upgrade your core version? Most of my sites end up having horribly out of date cores anyway, so why bother?
• Even if it is so bad for site owners, why does the community care so much? Why is it referred to as "killing kittens"? Isn't that rather hyperbolic?
• Hacking core is so easy, don't we like taking the easier route to a problems' solution?
• Aren't there problems that can only be solved by hacking core? What then?