So there's some sort of difference in the neurological makeup of developers and business owners around the phrase "you don't have to pay me." Developers think that proposition decreases risk. Business owners think
exactly the opposite. It suggests that there's such significant project risk associated with employing you that the market forces you to self-indemnify for that risk upfront, which
virtually no other service provider they use does. (Separate from what your client thinks of it, it also puts your paycheck at the mercy of clients' ability to e.g. follow through on your recommendations. Clients generally
earn the results they get from working with outside consultants, just like they earn the results they get from working with their own employees. The ones who do everything in their power to make engagements a success tend to do better than ones who... don't. You probably still want to get paid when they... don't.)
I'm not totally opposed to some sort of variable payout mechanic to pricing, but the vast majority of my engagements are structured "I work X weeks at $Y per week." By the time I've sold you on the engagement, I should have been able to sell you on X$Y being an acceptable price to pay for the risk-discounted probability space of all possible outcomes to the engagement. (n.b. If you do variable payouts for anything, you need to figure out how to transfer a large percentage of the upside from the client to you for the math to work out.)
If I personally was selling you an engagement, and you said "What happens if this doesn't lead to an improvement in the business?", the very next words out of my mouth will be "It is entirely possible that this engagement will not lead to an improvement in the business. The vast of my engagements have been successes. Some of them, like the ones we talked about earlier, were incredible successes. Let's talk about ways we can be more likely to make this engagement successful. If you do not believe that this engagement is likely to be successful, we will not do this engagement." (I'd also independently decline an engagement where I thought it wasn't likely to be a win or would meaningfully damage the business in event of a failure. I typically work for companies with revenues in the eight figure range -- if they set fire to my entire paycheck, nobody goes home hungry.)
As to what you personally could offer for risk reducers, absent a history of doing exactly this thing before, I might suggest reaching back into your portfolio of other things you have done and showing off ones which demonstrated likelihood of success. In my first few consulting engagements, my main portfolio piece was "similar work which I did for my own business worked out well, as evidenced by a few years of blog posts; here's a few I like." After the first few engagements, well, BCC was no longer the most credible piece of evidence I could point to.