The demand for safety deposit boxes in Bangkok far exceeds the supply. But rather than just raise the prices of the boxes, Thai banks use this supply/demand imbalance to try to extract as much money as possible from customers (while appearing to have reasonably priced safety deposit boxes) by requiring the purchase of unnecessary, unwanted, ridiculously expensive insurance.
You said that your bank told you that they don't have any boxes available. Just for fun, why don't you go back and tell them that you have decided that you want the insurance, and see if a box doesn't suddenly become available.
Anyway, don't fret, as there is another solution: A private safety deposit box company. Here is the company that I have been using for the past couple of years.
https://www.cblockers.com
I have a small box there for a reasonable price, and they are very nice and professional. It is not as close to my home as my bank is, but it's right in the center of Bangkok, which is not an issue for me as I only go there a couple of times a year. And if this one doesn't suit you, there is another such company in Bangkok, as I recall from my research a couple of years ago when I was in your situation.
Good luck, and buck the fanks.