Firstly, I'd start asking whether a $19.95/month shared hosting* account is a "reasonable" place to store $13k worth of (effectively) cash. I'd be _very_ careful if I had that sort of folding-money-type-cash on hand, and would under normal circumstances automatically deposit in a bank account to mitigate the risks involved with carrying it around. And I'd usually take steps to not ever have that sort of value of cash build up or be required - the only transaction I've ever done of that sort of value in cash is selling or buying a car from an individual - and that's always been a direct from transaction to the bank type of arrangement.
If I had enough bitcoin value that it'd hurt to lose it, I would not (at least now in hindsight) store that on a machine that other people I don't know/trust have root access to. Maybe I'd keep my wallet on a usb stick in my pocket or in a safe at home? I think though that at somewhere near the $13k value the "right" thing to do is convert it to cash and take advantage of the existing banking system and its time-tested security and insurability.
(* Which is fundamentally what a linode VPS is, at least from anyone with access to the hypervisors point of view.)
With respect for #3 it would be reasonable for a bank safe deposit box to contain a $100,000 ring maybe but not to contain a 10,000,000 ring.
There's a saying in many businesses with different variations:
"Price, quality, speed" pick any two.
So this would be:
"Price, security, bandwidth" pick any two.
People pick on price and bandwidth security is taken for granted to be commercially acceptable. The colo can easily figure out price and bandwidth they are clearly defined. Losses from a security breach not as easy - to many variables. Same reason insurance companies love to write life insurance but hate to write disability insurance. Life insurance is absolute (you know when someone is dead and tables exist to compute probabilities on when they will die). Disability is open to interpretation, fraud and other things. It's not black and white.
You have to trust somebody at some point unless you're keeping the server locked in your own closet. It seems really bizarre to me to say that a hosting provider doesn't have a responsibility not to steal your stuff.