Can't comment on why the original poster wants enduro forks on the Duke. But for me, I run a group for riders dedicated to custom scrambler builds. We do it for the fun of it. We have Ducati's, MT03's, a W800, Triumph Bonevilles, SV650's, basically any naked bikes that have been converted to run a mix of road and dirt (aka Scramblers). It's incredibly fun and you have just as much fun riding to the dirt roads as you do on them. I've had plenty of Scramblers in the past as I tend to build, ride and then sell every couple of months just to keep things interesting. For my latest build, I specifically picked the Duke 390 for a number of reasons.
Size and weight - It's small and light. Much smaller and lighter than what the others guys in my group run. I'm a small/light guy and I don't like wrestling with 200kg bikes.
Ergonomics - It has a great riding position which lends itself well to off-road style riding, albeit it's too cramped to be able to comfortably ride standing on the pegs.
Power - Just the right amount to make road riding fun and not so much that you're constantly wheel spinning whilst on the dirt.
Ground clearance - No nasty header pipes or oil filters hanging underneath the engine, and you can buy bash plates already made.
Suspension travel - This little thing has 150mm front and rear. That's well above average for a road bike. It actually has more than the CB500X and Versys 300X.
Price - Second hand these are dirt cheap. I got mine for $2,600 AUD because it had a few scratches already from a carpark fall.
So those are the reasons I chose the bike before actually owning one. Once I bought it and test rode it a few things were realised. On road this bike is incredibly fun and one of the most fun bikes I've owned. The rear suspension felt cheap and harsh, but other than that I couldn't fault it. Based on this, I sourced an R6 shock and threw it on expecting that it would not only improve road riding performance and comfort, but that it would also benefit off road riding by being slightly longer and allowing me to tune the damping for additional comfort. Then it came to testing the bike off road. Almost everything from my above list was spot on. Size, weight, ergos, power, ground clearance. Where it fell quite short of expectations was suspension travel at the front end. 150mm should be plenty of travel. At the rear it was more than enough to never bottom out even loaded with a bit of gear, but when you take into account the highly excessive sag (especially for myself as a lightweight rider at 75kg), I was left with an effective travel at the front end that was far short of this number. This should be an easy fix. The travel is there, the valving is competent enough, it just needs more suitable springs. And so I've sourced some 0.75kg/mm fork springs to swap out with the 0.62kg/mm standard springs. If I set these up with about 30-40mm rider sag then I'll have an addional 110-120mm usable travel at 0.75kg/mm before I bottom out, which is significantly better than the 75-85mm of travel at 0.62kg/mm that I have now. This should be plenty enough to allow my bike to do what I'm asking of it and be a **** of a lot of fun to ride while doing so.
The reason I've specifically picked on the front forks of the standard Duke 390 is because I haven't had this issue before with any other road bike being used off road. And all of the other road bikes I've ridden off road have had LESS suspension travel and so my conclusion that the standard front springs are very sloppy is based on the ease at which they bottom out especially considering their long travel. If you Google or search on this site for the standard front sag numbers people are getting on this bike you pretty much come up with nothing, but take some measurements yourself and you'll be surprised.