Of all the jobs in the game, Bard is the one that most benefits from having a parser. It is nothing like as simple as 1 song beating another.
If your parties average accuracy is below roughly 75% without Madrigal, the addition of Madrigal will outperform min or march. However if there is consistently more than 8% Haste on each DD, march begins to pull ahead. However march has 0 benefit to WS DMG, thus would likely need more like 10%+ Haste on everyone prior to march to exceed madrigal. (At least for 520delay(*))
While stacking atk you'll eyeball bigger numbers, on parse it also under performs without the necessary acc.
Not more than a week ago in a DRG burn in the early 50s I was sent a /tell from one of the members demanding I cast Mad/Min (presumably from the habit of having Mad/Min). Despite pointing out his accuracy with Mad/Mad wasn't parsing over 70% and even the most well geared in the party was just above 80% he basically claimed I was hurting the party.
Subsequently I changed songs for a bit and we didn't see past chain 5 for about half an hour.
Later switching back to Mad/Mad, we were back to breaking chain 6~7 every other pull, peaking at chain 9. I wouldn't personally say 20.1k/hr in the 50s sucked tbh.
Moral of the story, adapt your songs to suite the needs of your party. There are no songs you should just stick to, nor are there any you can write off. Bard is about maximizing a parties potential, and making up for there shortfalls. Not deliberately ignoring there shortfalls because they don't live up to your standards.
I mean, would you refuse to ballad a mage if he didn't have a decent Hmp set?
ACC is easily boosted with sushi
Your logic is flawed. Madrigal quite often allows a DD to switch from sushi to meat/curry which will render a higher atk bonus than Minuet. (*)For a 520 delay weapon
8.6 seconds a hit
Madrigal (30acc, 15% relative)
867 second to hit 100 times
90% hit rate, 90 hits
867 seconds to hit 113 times
75% hit rate, 84.75 hits
11%March + 8% Haste
867 Seconds to hit 120 times
75% hit rate, 90 hits