I think I've stated my opinion on (battleship) duels before, but may as well say it again.
Personally I think battleship duels, especially ones where it is explicitly specified there are no limitations, are catering solely to the pilot with more SP and ISK to invest into the ship. To me it's less of a question of skill and more about a numbers game with battleship 1v1s (if they are fit competently). It's not fair or equal by any stretch as whoever has more ISK to leverage can come out on top in most cases (HG slave sets as a perfect example of this imbalance). Where is the fun or challenge in that?
I see why some characters would choose to challenge someone to a BS duel IC, but as has been touched on by several others there are a lot of reasons why someone would refuse. In this case it's hard for me not to see it as a tool to paint someone as a coward. They refuse the duel because they can't even competently fly one, think it's a waste of good crew, or some other consideration and are publicly labeled as cowardly by the challenging party. No real complaint about the tactic there, as it's a perfectly valid propaganda approach. That said, if it's used during a debate to attempt to marr someone's reputation and invalidate their points it turns into a tool for dishonest debate. If a character wants to do that, all well and good, but don't expect anyone to want to engage in discourse with that character if they know there is a chance of it devolving into a similar situation.
On a totally different point, Misan were to ever accept a duel it would have to be a Frigate duel. Risking crew for some point of honor or pride is a foolish choice in her mind. Frigate fights are much more of an equalizer of skill points and there's quite a lot of variety in the ship hulls at that level. I found it more challenging to develop a good counter ship at the frigate level.
Edit: To address Miz's question after I already wrote this:
Assuming roughly equal pilot SP levels and ISK invested into the BS, there can be some fun had by both sides during the duel. OOC it's just about throwing big ships at each other and seeing who comes out the victor. Nothing wrong with that, as I've said above I just think it's not as much a test of skill as SP/ISK in more cases. I've enjoyed watching random BS 1v1s in PvP videos, but those aren't usually arranged (though the bits where they get outnumbered are better
).
As for IC, not really sure myself. They can be a way to establish dominance or superiority I suppose. Not all capsuleers care that they are risking crew or that winning a duel doesn't kill or defeat their opponent. Lots of options for why someone might enjoy them IC.