Almost every broker that sells bike insurance will use 4th Dimension if you do not want to claim on your own insurance and use your own repairer. 4th Dimension pay the brokers to see the claims in the first instance, and ultimately they present this options as an alternative to claiming on your own policy, assuming you have comprehensive cover, if not, then a Third party claim is your only option. The main issue is people generally have no idea what they pay for when it comes to insurance, and have a lot of common misconceptions. You pay insurance for them to pay you, end of story, fault or non fault. Insurance companies have never promised or never will look to deal with another drivers insurance to get your garage paid to fix your bike, they will pay the garage to fix your bike, subject to you making a claim against your policy, fault or non fault does not come into it, If the accident is indeed agreed as non fault by all parties concerned, your insurer will make a full recovery and the claim closed non fault. If no one is making a claim on your policy, your insurer have no need to talk to a Third Party Insurer, simple as that.
4th Dimension will deal with the third party insurer to get you paid directly via them, your insurer who you pay your premium to do not do this, and 4th Dimension don't do this for fun or for anyone's health, and are a business.
If you have an opportunity to settle outside of insurance all together with the other driver directly, this will always be your best option. Otherwise you can claim on your own policy or deal directly with the third party insurer yourself.