Wall of text, bear with me...
As a beer judge reading this I can say I have felt the same as you at times but have changed my opinion through experience. I originally thought the whole thing was a scam but now I realize there are some very important factors in the equation to consider before discrediting the whole system.
But to address some comments I have read before I explain why I think it is still a useful system:
-Judging normally isn't from memory. There are copies of the style guidelines (or at least there should be per competition rules) at every table. I have seen judges "wing it" from memory but every table I am at I pull out the guidelines and read back the description if they say something out of line.
-They can usually choose the category they judge, meaning they shouldn't be judging beer styles they hate. If they have to because of numbers (or lack of) then they judge the beer by definition not by preference. In a perfect world this happens, in the real world you will get people complaining they didn't want to drink *said random style* all day. Even though this happens, 99% of the time I have been on a style they are still impartial. The remaining 1% we get into an argument at some point, everyone steps back and re-calibrates and we get back to definition.
-You don't get drunk. I normally work one of the largest competitions in the US (Indiana State Fair) in addition to the small ones and have judged over 50 beers in a day, other judges have done more I'm sure. You have a water pitcher, neutral snacks like crackers and as many breaks as you want. It's hard to get drunk writing essays for 6 hours, try it some time! Plus many entries have problems, you would be a masichist if you wanted to get drunk like that.
-Scores don't start at 50 and get deductions. Look at the score sheet, most beers belong around 30(very good). Competition is steep. If you get a 35 you are above average. Generally anything above 45 is reserved for beers that are so rediculously good they break the mold. Beers that take what a style is and find a new way to exemplify it beyond what has been done before but make you think "This is what it should have been!".
-It matters what competition you enter. The smaller competitions will have fewer, less experienced judges who are overworked. The bigger ones will have Grand masters and experienced professionals divided between tables evenly to take advantage of their expertise. If you don't like your result I highly recommend you submit to a larger even out-of-state competition.
Finally I will say not giving feedback is a major issue in BJCP and people know it. Before every competition the organizers normally give a mini-speech about how you paid good money to get answers and if we want better beer we need to educate people. Despite this some people still ignore it. In my opinion they shouldn't be judges. This brings me to my next point...
-You will at some point have a bad experience in a competition because of an individual. Beers are judged by people, some of them are arrogant or lack enough knowledge to be there. The vast majority care about beer and the people that make it. I am sorry you had a bad experience (I have been there too), don't take it too seriously. Try a different competition and you will be surprised.
Now the reason why I still do them. The one truth about the system that makes it worth while is that simply the best beers really do win. Your score is just a number. It could be 26 in one place and 36 in another but at the end of the day the best beers always win. Don't focus on feedback like "hops" or "sweet", if you get a moderate score with little advice that really means you should look at your recipe. Get a odor-free plastic cup, a couple of friends and really tear it apart. Try to blend the flavors and tweak the components so they work together. Buy a commercial beer and taste it side-by-side. If this sounds like too much work then maybe competitions really aren't for you, but you don't have to stop making great beer at home for yourself.
If you did something bad you will get a very low score and they will definitely say something about it. If you did great ignore the praise and focus on the negatives to make it even better. Finally, even if your beer was great in the keg and great in the bottle you have in front of you the one they got might have gone bad. It happens, mixups are EXTREMELY rare. You can either enter it again or tweak your recipe, bottle it over a month in advance and taste it before you send it.