The turn over is really just related to heating and filtering the water. I don't think 10x return is going to keep much of anything in suspension in the tank or sump, it just isn't that high velocity. You probably only need more than a few times turn over to heat it. Filter stocks will obviously have better performance with doubling or tripling the passes. The Carbon and GFO or other filter media will almost certainly achieve their daily goals in a just a few passes an hour as well. Since the skimmer has a fixed flow rate I guess I don't see incredible gains by increasing the flow rate through that chamber as well. I am sure that getting 10x would increase performance on all of these elements but by what degree and how much are you willing to spend?
On a Triton system, they don't always say why they do things a certain way so we can only guess but I can see some potential benefits to a true 10x. First, with Triton I think we are transitioning from the fuge being a supportive filter to being the primary filter, not only is the fuge responsible for a majority of the nitrate and phosphate reduction there is a very reasonable chance the algae may actually prefer ammonia as it's nitrogen source. So this is a critical filter and unlike media reactors and skimmers which often have fixed flow rates regardless of sump turn over, the return pump and overflows are the feed to this important filter. So I would think of it as passing the system water volume through a specific filter 10x an hour which is a real thing rather than just 5-10x sump turn over which is a guideline without out much thought to the system or equipment in it.
I think in some ways this gets to the heart of why some reefers have success with "methods" and others don't. So often each component of the method gets debated and the individual reefer ends up passing on elements or adjusting it in a variety of ways. The net result is no longer the Triton method, it's "Ryan's method". For this discussion, I would say if you decided to change the method to your own desires and run 3x turn over and don't have the desired success I would certainly consider following the actual 10x recommendation for the primary filter before determining if the method works for you. It might be that 10x turn over is not possible and you just need to do your best and adjust or try something different. There are a lot of system designs and methods that work