Third party assures the purchaser the design meets industry standards regarding safety. By safety, I mean little to no risk of fire. They, as you likely know, do not care if the thing works as long as it does not have any fire hazards.
As far as this being required, it is not required on the surface. However, your local authority may require the device to be approved by UL or CSA or your end user. There are also plenty of markets available that could care less about the third party certification (I wont reveal these sources-hehe).
I have not heard of any cases where certification or no certification had any affect on the outcome of a lawsuit. Although, I am certain there is cases to point out. Having the certification tells the court that you took reasonable steps to assure the safety of the product. With some standards, it is easy to prove compliance with the standard even though you never actually sent it in to the agency for testing. This could be shown using your own testing, evaluations, etc.
Myself, working with UL508 alot, have to say that generally it is money going down the drain to send it in for testing, especially with the rising costs and lead times to get it through testing. If there was few cases where this certification did not help with a lawsuit, I would say it is really a rip off for the seasoned engineer. If your making a new product that falls within a different category or are not familiar with the standard (intimately) then it is probably money well spent to make sure you have the safest product available to reduce the risk of a lawsuit.