Simplicity is definitely one advantage. People often grumble about the spacing between ratios on a 1x cassette, however, in order to maintain perfect cadence on a 2x or 3x you would need to change gear on the front at the optimum point and I could rarely manage that. 1x removes that from the equation, spinning out? then change down, going is getting hard, then change up, simple. My riding is mostly 80% off road and to be honest, off road or on, I really don't notice any large jumps in gear ratio or gaps. I don't use Strava or slavishly record my times, I ride to enjoy my self and explore, so for me 1x is perfect.
Another point that others have bought up is the quality of gear changes, well I've ridden the bike all through the winter in the forest and yet to adjust or touch the drivetrain aside from cleaning it. The rear mech is clutched, so no chain chatter and no front mech cage for the chain to rub against, just a lovely silent drivetrain. I've also experienced no thrown chains either, no matter how rough the terrain. SRAM double tap aside, every gear change is crisp and precise, the problem comes in changing up. I'm a bit ham fisted and double tap requires a slightly more delicate touch, so changing up the cassette I often over changed through pushing the lever too far, I'm getting there though! Down shifting is really nice though, one click and down the chain pops, no over shifting or delay, just a nice, crisp down change.