The argument in favor of a one year drop are many. If you had a certain level of performance while preparing for 12th class and JEE together (just taking this as an example, I guess it will be true for any other competitive exam as well), your performance will certainly be better if you don't have to go to school, you don't have to take all those school tests and board exams, and you don't have to study "useless" subjects like language. Apparently, the data also supports the theory that the chance of a repeater are pretty good. If we look at yearly Advanced JEE reports, one finds that among those who are admitted to IITs, about half are those who passed 12th class that year, and half passed 12th class in the previous year. If we look at media (including social media), one finds many stories of people who succeeded in improving their performance in their second attempt, but hardly any stories of people who did worse.
So, shouldn't this be an obvious thing to do. With life expectancy of 80 years and rising, what is one year, if you can have a much "better" career afterwards.
But there is a problem. When we say that 50% of an IIT class is of repeaters, it does not tell us how many of them had succeeded last year as well. How many of them have improved their ranks substantially. If you are willing to invest one year of time, and resources (for coaching, for example) and lost wages for a future one year, it better be for a significant improvement in ranks and not a minor improvement in ranks.
Let us consider a student who has received a rank of up to 8000 in Advanced JEE this year. (I am using all examples of unreserved class, but same arguments hold for reserved classes as well.) This student could have received an offer of admission to Earth Science program at IIT Kanpur, and if he barely studied enough to pass all courses in the first year, he could shift to any program that closed at 3600 or later (through the program change policy of IITK after one year). If he worked hard in IITK, he could get a change to a program which is closing at 2800 or higher this year. So an improvement of 5000 ranks next year is completely useless since what he will get next year, he could have got that after joining IITK this year itself. Getting a better CPI to be able to get the top three programs - CSE, EE and Maths - is hard, but so is to get a rank within top 1000 next year. You can't depend on change of program after first year, but you can perhaps depend on it more than you can depend on getting a top rank in JEE Advanced (and being in top 1 lakh in JEE Mains as well).
Does it make sense to drop a year if you had a rank giving you an unpopular NIT seat and you hope that next year you will at least get a popular NIT seat. I still wouldn't recommend dropping a year. There are several institutions outside the JOSAA system which are as good but have significantly lower cutoffs for admission because they do their own admissions, and in some cases are far more expensive. I am talking about places like LNMIIT, DAIICT, etc. These are as good in terms of education as most NITs, but are not preferred because many students and parents go for brand and not quality, and also they will require an addition lakh or more per year. But remember, one year drop has costs too and as I said above, not just cost of coaching, but also cost of lost wages. So, go for a private place which is as good as an NIT.
So the only situation in which dropping one year may make sense is where you are sure of not a small improvement but a very substantial improvement. You had a JEE rank of 75,000 this year, and you are expecting a rank of 15,000 next year. Or you had a JEE advanced rank of 20,000 this year, and are expecting a rank of 5,000 or better next year. Small improvements are not worth this investment.
But what is the probability of major improvement. Very small!
While the argument stated at the beginning (that we will have exclusive focus this year) is attractive, one also has to see if one will continue to have motivation to study hard for one long year. Would you not feel lonely since most of your school time friends have gone to colleges. How would you answer your neighbors, relatives and all sundry uncles as to which college you are studying in. Would you not be stressed by the thought that you might perform worse than this year. In the coaching class, everyone is a new face, no one whom you had known for years in school. These conditions can break the motivation level of most people. And once your motivation is gone, so is your chance of significant improvement.
So when should one drop a year.
If you can identify a reason (other than giving 12th class and JEE together) that caused your JEE performance to be worse than what you believe to be your capability and that reason is essentially a low probability event, then it would make sense for you to drop a year. For example, if you fell ill on the JEE day or in days leading to JEE affecting your last minute preparation badly (otherwise, you were doing well in your coaching exams). You had a family crisis (like a major accident or worse, a death) which obviously would have affected your preparation and performance. Or any other big reason like these.
Of course, situation of every student is unique. Whether they can maintain motivation for entire year will depend on their will power. Whether something seriously bothered them and affected their performance will have to be decided by them. Whether it is possible to go for a much more expensive option for education will depend on their financial background. Worst case scenario will be different for each student. For example, someone who has performance extremely well in 12th class and can get admission to a good college based on that even next year is taking a smaller risk and hence is not likely to be affected by stress through the year. So take everything said in this article with a pinch of salt and see what applied to you and what doesn't. But, in general, if there is even a slight doubt, don't drop a year.