Naw, tenants insurance is entirely reasonable in my book. That’s not meant for small things. That’s meant for huge disasters like if you cause a fire that burns down the entire building. The liability insurance is the only part they usually care about. Fortunately, it’s usually relatively cheap, too.
If you didn’t have insurance, they’d just need more insurance themselves and they’ll pass that buck on to you. At least with renters insurance, you can get some coverage for your personal belongings, too.