I have an IGH on my current bike and my last one. I didn't know it existed as my bikes from age 12 had deraileurs. I ended up spending more on the IGH because I remember how annoying it was to put your chain back on when it came off. The grease never came off your hands.

A chain guard or chain case is probably sufficient to deal with grease on an IGH bike. I didn't have a problem with my partial chain case setup. It was easy not to get grease on my hands.

Personally the big thing for me: feeling safe on the road, having a bike I can wear normal gear and a great looking and stylish bike pushed me over.

The belt drive? Not so sure. Seems way complicated.