I have a Mezzo 10 speed with shimano 105 and am considering fitting a Rohloff 14 speed hub. Anyone out there who's done this. What practical advantage are there in fitting the Rohloff ....

This is an expensive conversion, and while there are big fans of IGH here on the forum, I still believe that based on weight and efficiency, derailleur systems are better for sport and touring use. OTOH, having everything is a closed can is great for commuter and utility use, and may also make sense in harsh environments.

Based on my preferences, I consider IGH most practical in 3-5, or maybe 7 speeds, but don't see a need for something like a 14 gear IGH. But that's just me, and everyone needs to decide for themselves.

Before converting, understand that IGH on a modern vertical dropout bike means you'll need a chain tensioning device, which is somewhat counter to the spirit of IGH (my opinion) so I wouldn't convert a vertical dropout derailleur bike. If I wanted to build an IGH bike, I'd start fresh, with a frame more suited, either by virtue of horizontal dropouts, or something like an eccentric BB, or the Paragon moveable dropouts.

Isn't the Mezzo a folding bike? I'd imagine the only specific advantage to your bike would be not having a rear derailleur to stick out and get bent when the bike's folded up on the luggage rack of a train or whatever.

Obviously there's also the reduced maintenance and longer chain life with a singlespeed chain, not to mention the ability to shift gear while stationary, but you'd get that converting any bike to any IGH.

I am not familiar with the Mezzo, but it apparently lacks horizontal dropouts to adjust chain tension. This necessitates fitting a chain tensioner (show on the photos of their IGH model) which to my mind nullifies much of the compact "all-sealed" advantage of an IGH.

First, consider the application. I love Rohloffs, I have two of them, one in a cargo bike, the other in a recumbent. Both are bikes that need the gearing range offered by the Rohloff, and the cargo bike needs something robust, and Rohloff fits the bill.
But my other bikes are fitted with 2, 3,5 and 8 speed gearhubs, and for what I use them for, a Rohloff would be serious overkill.
For regular road riding, on anything but the biggest hills, you might be surprised how well you can do with a 5 speed.