To force you to use a particular insurer is anti competitive. Further, in the past when I have used self store I have not been obliged to take out insurance at all.
I have no expectation of them being liable for any loss I incur unless it's due to their negligence. Legally they cannot contract out of their obligations for negligent acts anyway.
I would like though to retain the right to choose if and with whom I take out any insurance.
They also fail to show their "compulsory" insurance prices on their website or to include them in their quotes - again I don't believe this is legal.