[@ImportantNobody]
In spite of everything I'm about to say, I'd like to remind everyone that I want to [i]put this thread behind me[/i].

[quote=ImportantNobody]
I see dice rolls being useful in certain rare circumstances. For example, if someone is shooting at someone else and you are up in the air if bullets would be hitting and how many. Sometimes it's a struggle to be fair and logical in such circumstances, leading me to worry if I'm being unfairly accurate or, if I'm dodging, unfairly dodging everything. I tend to just take the hit if there's questionable stuff. 
[/quote]
This is where things can get a bit more understandable, but - as I mentioned multiple times in this thread - using dice for this sort of thing becomes more unreasonable the more powerful/complex/skilled/intelligent/etc the characters are. For example, I usually work with [i]very[/i] high tier and broken characters due to be my story project's setting being incredibly powerful -- most of my characters are well and truly beyond the point where anything luck-based could ever impact them.

To put it into perspective -- the GM used the example of how many competitive role-play duellers will make their characters dodge something even if there's only a 0.000000000000000001% chance of successful doing so; however, this is actually [i]justified[/i] if the character can manipulate probability and causality, which even the [i]bottom tiers[/i] in my setting can do. I should also make a point that - despite how powerful my characters are - I have never role-played a duel that utilized even a fraction of their true power, and my opponents were also given similarly powerful abilities in order to allow fairness.

When my characters dodge something, there is always a well-thought-out strategy and concept behind it.

[quote=ImportantNobody]
As a main fight mechanic it's not preferred if going for realism but could keep things more exciting where you aren't sure how it will turn out and have to adapt. Could also be funny if you roll a 1 and have to come up with some rediculous reason why your character failed so badly.
[/quote]
You've just described one of my main gripes for why I believe using dice rolls actually ruins realism and stifles writing - not just destroys competitive play - because I've frequently had to write my characters incredibly out of character in the past in order to cater to a dice roll -- out of character writing is one of the top definitions of bad writing in my eyes. You're not just 'adapting' to the dice rolls if you have to blatantly write something your character would never do in order to work with them, which happens [i]far[/i] too often.

[quote=ImportantNobody]
Not using dice and instead going for story purposes and rule of cool would be best if you and your opponent aren't competitive. Then I wouldn't have to worry about accidentally abusing stuff and being op because they would be okay with the outcomes.
[/quote]
I believe - in order to achieve a truly ideal balance for free-form role-play - both players need to have some level of competitiveness while balancing it out with good collaboration and sportsmanship. I think the best way to describe a good free-form role-player compared to a bad free-form role-player would be to think of them as a person who has an adult debate in comparison to someone who has a childish argument.

Also, as I've mentioned several times in this thread, I've met many role-players who actually use dice rolls and stats [i]specifically[/i] because they wanted to use them to power game -- they sucked at free-form role-playing and wanted to exploit these mechanics.