What are the tradeoffs?When examining tradeoffs, it's helpful to look at extremes. If fewer gears are a benefit, why doesn't everyone run single speeds? They're lighter and less complicated than even a 1x11 setup.
If you've ridden a single-speed bike, then you know that climbing can be a challenge if you lack a good strength-to-weight ratio. This can be a challenge for heavier riders and it becomes more of an issue as you age, when power generally decreases.
Another factor with pedaling at slower cadences due to a lack of power or gearing choices on single gear is that it puts more strain on the joints, which can lead to injury.
The other part of the equation is downhill riding. Single-speed riders will not be able to spin a fast enough to keep up with riders on a geared bike. They will "spin out."
Though the single-speed discussion is an extreme, consider the same principles as you will lose several gears going to a 1x11 setup.
The tradeoffs for the other extreme are just as important. If one gear is too little, why not go with a triple chainring in the front and 10 or more gears on the rear cassette? The tradeoff here is weight and the potential for mechanical problems, such as chain drop or the increased likelihood of mis-shifting.
Benefits: It's great to have multiple choices. You'll have to decide what tradeoffs you want to make in order to optimize your riding experience.
What matters to you?What "performance" means to each cyclist can be slightly different. The definition of performance depends on your individual preference for simplicity, bike weight, terrain, distance and your individual strength-to-weight ratio.
For one cyclist, a "high-performance bike" means the one that is setup to be as light as possible. For another rider, a high-performance bike is the one that will produce the fastest time on a two-hour ride with short, punchy climbs. The best gear choice for you is always one that fits the combination of your preferences and goals. No single answer fits all riders.