In all truth - it doesn't protect anyone, rather it enables those with whom you conduct business (including yourself) to mitigate any losses sustained.
Remember, that before your insurance will pay anyone - a claim must be filed by you or a suit must be filed by them, where you in term solicit your insurance carrier to intervene on your behalf.
The function hall wants you to be insured so that if THEY are sued - they can in turn enjoin you in the suit. Any resulting judgement or settlement would then be split among the enjoined parties and their insurers, thus reducing the exposure of the venue.
You NEED the insurance if you have any vulnerable assets or family you wish to shelter. If you are young and have none - your risk is probably limited to a future garnishment of wages.
But being the insured party doesn't always work in your favor.
Imagine this scenario: The fucntion hall sues the bride, and you along with her for property damaged that ensued during the event. Not only is the bride not likely to be insured for this, but her lawyer is likely to recommend deflecting all of the blame to you - making you and your insurer 100% liable for any judgement or settlement. Failing that, they will sue you to recover whatever liability they incur.
The reason some venues never ask for a certificate of insurance is because their own policy already provides coverage for liabilities incurred as the result of guests and vendors operating on their premises. Others, use the insurance requirement to lower their own insurance premiums by requiring other vendors to share the risk.
Now for the advertising.
You should not promote yourself to clients as "fully insured" unless you are in a business that typically places a direct laibility on your customer or their property (such as roofing and painting). Otherwise, you may be inviting people who "fish" for insurance settlements.
Despite that, you should still be able to converse intelligently with venues and other vendors about these risks and the protections you have put in place. There is no law that requires you to have liability insurance in an unlicensed profession where you have no employees. As such, you should not just agree to make a venue an additional insured on your policy simply because they ask. You are always free to negotiate your own terms. You do not want to inadvertantly find yourself being enjoined in a suit over something that happened at the party downstairs - simply because you were in the building and have insurance.
The best way to present your insurance to a customer is to let them know that by protecting yourself financially - they can be confident that you might still be in business next year even if, God forbid, an unfortunate incident occurs this year. If you are also insuring your equipment, then in the same manner you want to demonstrate the depth of your resources and ability to recover from a sudden loss.
Consider the following question and the difference between two responses:
What happens if all your equipment gets lost or stolen?"
A. The insurance will reimburse me for the replacement cost.
B. I have a friend who will let me borrow his.