Insurance companies are not in the business of losing money. So they did some calculations and decided it is a good risk and sell you the insurance. It means that you are usually ahead if you don't buy the insurance and can afford to replace it yourself if lost. Otherwise, you end up buying insurance for too many things (TV, your bicycle, your fridge, etc.). It adds up.
The bike is expensive for me. If I lose it, it would take some time before I can buy another one. But I figure if I lose my bike, I can save up to buy another one, and considering the risk, I should be ahead because the insurance is not in the business to lose money.
You need to read the fine print to see if you need to file a police report before you can recover money from insurance. Then decide if you are willing to spend the time to do so. Is the police coming to you or do you have to take the time to go to a police station to file a report. How much is a day off work worth to you? If you lose your bike on a campus, is a campus police report good enough or do you need a town police report?
Also, if your deductible is high - then you can probably only recover if your bike goes missing. Will you recover if there is no evidence of force?
It is not like once you have insurance you can bike around without locking your bike and leaving the keys in - I wish it was that simple. So you have to find out what duty you have (lock bike, police report, etc.) before you get reimbursed. I can see if you have house/car insurance costing a lot and you are a long-time good customer then they may be more lenient when reimbursing your bike. But if you just buy bike insurance and your bike mysteriously disappears without any sign of force that they may be more careful.
I usually try to self-insure - meaning not buy any insurance except for stuff that I can't afford to replace easily like a car or a house.
Maybe we should start another thread - how many people actually received an insurance payout after a bike is stolen and do they feel that the amount received was adequate considering the time and effort and money involved in getting insurance?