I don't think it's just the fat tires that make a difference. I would imagine, if one only rode road bikes and then rode a full suspension mtb they would find it equally as fun in some regard. The difference there is that a rigid platform allows better travel potential (less squish, weight and better geometry).

I guess it's like owning a 4x4 jeep (a real one,not just a looker). To the common eye they are impractical, hold less people, can't haul much, poor aerodynamics and COG... but, if you own one I imagine you just like driving it and look forward to finding places to take it.

We can look at touring bikes as practical platforms for hauling ourselves and our gear from A-B but they can also enhance and shape the journey as well. Like someone who chooses to tour on a penny farthing or a unicycle. Why? Just because.

In my case I found my endurance bike covered the road and gravel scene pretty well (as I don't do heavily loaded touring atm). That left the off road genre open and I didn't want to be limited in terrain by tire size so I sought a bike capable of wide enough tires to cover the far end of the spectrum. I wouldn't want it to be my only touring bike though as it is limited for road use. Except for snow and soft sand, I think 3" probably is a better choice than 4". A 29x3" ECR for example (or any other plus bike like it) can also drop down to 2.5 smoother mixed surface tread if one wants without too much BB height sacrifice.

A suspension fork and 2.5 mtb tires can probably handle most off road conditions and if distance traveled each day takes precedence over all terrain then it may be a better choice - the suspension is the trade off for the wider tires. But those tires won't handle swampy or sandy conditions as well. That I think is the big decision. Which takes more precedence.