Here is an excellent technical reason not to: maybe you simply can't put the 11-* cassette onto your hub.
For instance, if we consider Shimano HyperGlide: the Shimano cassettes which have 11 cogs require the HyperGlide-C (compact) style hub, whose splines do not extend all the way to the edge. The 11 cog does not actually go onto the splines like the other cogs. It sits on the end of the hub, and partially goes onto the shortened splines. It requires a special variant of the lock-ring, which comes with the cassette. On the other hand, 12-* cassettes fit these compact hubs. For example, I'm using a 12-23 range CS-HG50-8 on a HyperGlide compact hub that previously had a 11. The shortened splines of the compact hub still adequately grab the 12 cog, so it doesn't rotate freely around the hub. (By the way, there you go: I'm a a live example of someone opting for 12, after using 11! I still just rarely use the 12).
Related to point 1, the fact that a special hub is required tells you something: the 11 cog is technically inferior. It is on the specification fringes of what will possibly fit onto the hub, which is a bad place to be. It has to be constructed with partial splines, because if it had full splines to go onto a regular hub then the cog's hub would be too thin and weak. The splines not going all the way through the cog's inner hub allows there to be more steel to hold the entire part together. There is another way in which the 11 is inferior: you will commonly find, on even a lightly worn cassette, evidence that the chain plates are making contact with the 11T cog's hub! In other words, chains do not sit very well on the teeth of the 11; they ride the inner ring. If not when the cassette is new, then eventually. The 11 will likely be the first gear to start skipping when the chain and cassette wear. Since for many riders that's a big clue to throw out the entire cassette and chain, it may lead to unnecessarily frequent replacements.
A cyclist that rarely uses a 12 will use an 11 even more rarely; perhaps never. Any gears you don't use effectively reduce the number of gears in your cassette. If you have a 9 speed cassette but only use 2-8, then you really have a 7 speed cassette, with spacing and padding cogs that make it compatible with your 9 speed shifter.
Higher gear does not translate to faster. Your maximum speed over a short distance might not be achievable in the highest gear, in fact. One use for the highest gear is in fact to go slower, with a relaxed, slow cadence. A car analogy can be made here: it's like an over-drive gear that lets you work with lower RPM on the freeway, saving gas. (Car analogies are good, but they break down in one important way: car engines do not get tired, and do not have to pace themselves with regard to expected distance.) Just like a car, we can downshift on a bicycle to get more power. Yesterday, to catch a green light, I downshifted from 5 to 4 on my 12-23/8 cassette, accelerated, and outpaced the cars. Also, these downshifts have to be subtle: it helps to have the close gear ratios. To have close gear ratios, don't get a cassette which includes gears that you won't use! I was already pedaling at a decent cadence in 5; too much of an increase in cadence in the downshift would have been counterproductive: I would end up whipping my legs around, going nowhere.
The 11 tooth cogs have a purpose: they go with compact drive systems which have a smaller ring in the front, like 48 teeth (or even less), common on mountain bikes. They are also useful for bikes with smaller diameter wheels. The 11 cog against a 48 ring gives you almost the same gear ratio as 12 against 52. The 11 cog is thus a useful accessory for converting a mountain bike for commuting use in an inexpensive way (avoiding replacing the front ring). Throw out the 13-34 cassette and put in an 11-25, slap on "road slicks" tires, and maybe some fenders and possibly a rack, and you're good to go. If this is what you're doing, the 11 may be for you.
If you have a road bike with a 52 or 53 front ring, with 700c wheels and average sized pedal cranks, the 11 is probably a bad idea that you will regret, unless perhaps you're an elite cyclist with a "power plant" that works well with higher gearing.
Now I can understand why someone would choose a cassette based off of how many teeth the big gear has. Some people live in hilly or mountainous areas and desire a higher number of teeth.
Actually, the desire for more teeth in the cassette is only understandable if the cyclist has no front derailleur. Or, say, only two rings in the front. Otherwise, the desire is, well, still understandable as a desire, but not all that rationally founded. If you have three rings, there is no need for anything larger than a 23 cog in the cassette. With the small ring engaged in the front and the 23 in the back, you have a ridiculously low gear that feels akin to riding a five-year-old's tricycle. If there is a section of road you can't climb with that, just get off and walk. The only cyclists who need anything lower are athletes who do mountain cycling as a sport, involving ridiculous feats like climbing very steep sections of a rough trail. (They must stay on the bike, because that's the sport; a "normal person" either wouldn't go there with a bike at all, or would just carry it up that section of trail).
Bicycles marketed at the mass consumer market often come with ridiculously fat cassettes combined with three speeds in the front, which reinforces the consumer belief that these are good and necessary. It's not clear why this is, but it's probably for two or three reasons. It simplifies the use of the bike: the user can find every gear they need using the front derailleur only. Secondly, the number of speeds is often touted as a selling point to the general public. What happens when you put an 11-34 "Mega Range" cassette (say 9 speeds) into a mountain bike with three rings in the front is that the user ends up with effectively a 9 speed bike, with 18 additional gears that are either redundant or uselessly low. However it can be marketed in the flyer as a 27 speed bike. The large cassette also looks impressive, and consumers like words like "mega"; they think they are getting something special, or more for the money.