LL will never be able to dream up all of the possible scenario that T (or third party lawyer) could attempt to sue on. Unless you think requiring it will chase away good people or you cannot bury the cost into the rent ($10 - $20 /month) and remain competitive I would argue that you are taking excessive risk to not require it.
I'll check with my insurance agent about cost, but the competitive rental market I'm in at this point, I'm not sure taking on the cost myself and adding it to the rent is a good idea. I'd prefer to put it as a requirement for renting.
I haven't tried including because of something I read (probably this site) suggesting that it is a gray area f landlord pays for the insurance - something with the legality of LL insuring... but I'm not very clear in this. anyone can clarify if there could be legal issues if LL pays for T renters insurance?