There is nothing wrong with using carbonation drops. There are some advantages.
They give you a very consistent carbonation from bottle to bottle. Uneven priming sugar mix in the bottling bucket (forgetting to stir it without adding oxygen) can lead to uneven carbonation. Bottle bombs and weak/no carbonation.
You never forget to add them, which sometimes happens with priming sugar. Plus, if you do forget to add your priming sugar, you can always pry the caps off, drop in a tablet, and re-cap. (People do forget in their excitement to bottle to add the priming sugar.) Good reason to keep them on-hand as a backup.
If you do miss one, you only screw up one bottle.
No ability to control specific carbonation for a given beer style or preference. (rarely done, but still)
I think one of the best uses for carbonation drops is diagnosing carbonation issues. People who are getting consistent weak carbonation, over carbonation, or uneven carbonation can eliminate everything but their priming sugar amount/procedure as the issue. It's a nice diagnostic for when you have carbonation issues you have been unable to resolve.
I would also say that carbonation drops are a good tools for new brewers. As you get more experienced, you can graduate to using simple priming sugar. No shame in using them, even some experienced brewers use them regularly.
I usually boil up extra pale dry malt myself, rather than corn or table sugar. I do that because I always have dry malt on hand. There is no other use for corn sugar, and I hate to have a single-purpose ingredient around and table sugar can leave a twang, although I have never experienced that in just priming.