Go to jail? Seriously? Let's remain civil and mature in this discussion. Trial and error is a major part of proving theories
Yes there is
That is what proving a theory wrong is. It is finding a flaw in the theory. Theories are proven wrong via running several consistent experiments and monitoring the data. That is what a parser helps with.
This barely makes any sense as a question, but essentially a perfect rotation may not transfer well in to every fight (due to mechanics, jumps, adds etc). In order to illustrate my answer, I added square brackets into your quote.
Correct, that is how one comes up with their theory, by testing math. That said, due to the complexities of all the various skills, buffs that can be applied via your team and yourself, potions as well as debuffs and mechanics from given fights, it's great to test your said theory with a tool that will tell you if you're doing what you expect.
Well, you go in to the dungeon and use BoTD at one point several times and see your numbers. Then you go in and try using it at another point and see how your numbers change. This will help you understand when is best to use it.
For example, maybe I want to use Raging Strikes after I dot up, use paintflare/fester/fester/dreadwyrm, so I can have both raging, deathflare and x-drac pot up for another fester + ruin II + tridisaster and deathflare. However, in X fight, when I do that, I end up having 6 seconds of raging strikes ticking away while Y boss is jumping. Common sense would tell me that is a waste, but the parser can help me see exactly by how much of a waste. Perhaps it wasn't a waste at all if I deathflare before the jump, as all I lose is a few ticks on the dot. Perhaps, I need to hold all of those skills til after the jump and should just use Ruin I. Alright, so there are various situations, and I can probably do the math for every single encounter I run in to, but do we play this game to sit around with a calculator? Probably not, what is great is having a tool that shows us how are actions are changing with various attempts and ideas.
This depends how you want to read in to what people are saying. No one has claimed that a parser actually increases DPS on it's own. Everyone is saying it's a tool that lets you see if you are performing poorly, and will give you feedback with how changes in your playstyle affect this.
False, they can help you determine how your rotation is working and provide you the information which helps with adjusting. I am not saying a parser will improve your rotation on its own, but it will help towards that goal. Further, you can use the tool to see how you compare to other people of your same job and gear level, and ask for pointers when necessary.
Having a parser that gave you DPS once wouldn't help you improve your performance either. Parsers give real time data on how well you are doing.
That is not true and is offensive to anyone who doesn't. I have played with plenty of people who perform very poorly, but have no idea that they did. These people were not stupid, they just didn't think about everything the same way you or I did.
I mostly agree with this statement, even though it is factually incorrect. AoE can increase your DPS well above a dummy parse. The question is, is that AoE actually helpful or not?