I agree with you to an extent.
[TL;DR: Fiverr acts as an intermediary unlike LI, mainly beneficial to new sellers, up to Fiverr to see how to realistically implement this (and I hope they do!)]
Providing a link to your LinkedIn does create the opportunity for you to undercut Fiverr and marginally increase your revenue at the same time - and of course, any sensible business would not do this. But, off-Fiverr activity is very risky for both buyer and seller. There is nothing to stop a seller from running off with an upfront payment from a buyer, and there is nothing to stop a buyer from not paying the seller for delivered work. As far as I’m aware, LinkedIn doesn’t act as an intermediary payment system, nor do they have any resolution centre for transaction disputes like Fiverr has. That’s what I love about Fiverr. It is a regulated marketplace safe for both buyers and sellers.
As a new seller, it can be difficult to demonstrate trustworthiness. After all, buyers (particularly, new buyers) tend to follow the reviews. So, it would be helpful for sellers to be able to point to their LinkedIn to provide an air of trustworthiness - a LinkedIn profile with only five connections and no profile photo might be a red flag, but one with many connections, several experiences, and other info would act as a green flag to a concerned potential buyer.
Personally, as a new seller, I feel the functionality to link my LinkedIn account for buyers to see would give my gig a boost. Buyers would get that much extra confidence in a new seller and hence, it would be that much more likely you get an order. Once a new seller gets going, the LinkedIn profile matters less and less with public Fiverr metrics (more reviews, badges/levels, last delivery time, average response time, skill tests).
While I believe I’m now getting there as a Fiverr seller, I think it’s a great idea if Fiverr somehow lets you display your LinkedIn. As I mentioned, this would mainly be beneficial to new sellers, so maybe they could remove LI functionality after you have completed 20 orders or something. I don’t know, it would be up to Fiverr to figure out how they could implement it. Even if I become a seller with a five-star average after hundreds of reviews and it would help my competition more than it would help me, I would still support this idea.