I have found from experience on my 3x7 MTB that shifting a triple front chainring is useful if you do the following: I tend to use only the first 3 cogs in the smallest chainring so that is 3 very low gears for hills, grass, or just low speed stuff. I can use all 7 cogs in the middle chainring but tend to avoid the largest cog so that is 6 more gears. Then for downhill or just for slow cadence, I can use the 2 smallest cogs on the large chainring so that is 2 more gears. So that is 3+6+2 = 11 usable gears. What is particularly nice about this is the shift sequence (using S,M,L for chainring with S being small (granny), M being middle, and L being largest, and using 1 thru 7 for cogs with 1 being largest diameter cog and 7 being smallest) is (S1, S2, S3, M2, M3, M4, M5, M6, M7, L6, L7), is that there is never a shift to a gear more than 1 cog or chainring away. Going from S3 to M2 for example and also from M7 to L6. So this is basically a poor mans 11 speed bike but it works and fairly well too (from actual riding experience).
So my question is why do people tend to favor a 1x11 as superior to a 3x7 where only 11 of those are used as a described here? Is it because the 1x11 shifts better and with less complexity? How about the joy of doing successful double gear shift simultaneously that is fun. Also with the triple you can get very tall and very short gears without having to resort to very large and very small cogs, both of which cause some problems. Also shifting the 3x7 as I described here should have better chain alignment on average (assuming it has chainrings aligned with cogs 2,4 and 6 and the 1x11 has the single chainring aligned with cog 6).
Some answers here talk about ground clearance. My largest chainring on my triple is 42 which is less teeth than the larger chainring on some doubles.
Also to make my triple chainring shift sequence even easier, the rider can shift only 9 gears this order (L1, L2, L3, M3, M4, M5, M6, M7, H7). A biker can select front chainring sizes such that the shift from L3 to M3 and the shift from M7 to H7 is moderate (10% for example, such as 40 to 44 teeth). If I had an 8 speed freewheel I could get 10 progressive gears which would be good.