I was almost in the mood to play FF14 again

[Deo14]

If the issue is just "Shinten is used too much" then what needs to happen is a review of Kenki economy, including how much is gained through combos, and how much is spent via skills.
We already have SIX Kenki spenders, it's too much already.
I would say that Guren and Senei need to have their cooldowns and potencies reduced so that you're replacing more Shintens with Seneis. (halve each for each would be a decent start, still aligns with 2 minute window)
Then reduce some of the Kenki gains on weaponskills so that you're not capping on Kenki so fast. Have all weaponskills provide only 5 Kenki (other than Enpi at 10), then maybe boost Hagakure to 15 Kenki per Sen instead of 10 to compensate, and actually give Hagakure some potential use.

Kenki economy was already managed by Kaiten. Nerfing Kenki generation is solution, but by far not the best one. This would also need adjustments of the rest of the Kenki spenders, because if you needed to do some 2-3 GCDs to get enough Kenki for single Gyuten/Yaten, then that's a problem. You also generate less Kenki in 52-61, so it's this kind of nice gradual step up, but if you wanted to keep this, then the Kenki you generate in this level range would be abysmally low. This is not where potential complications end, the way you pool Kenki would be affected, you would need to completely recalculate potencies for SAM, if all GCDs only gave 5 Kenki, then it would be boring but also there would be no Yukikaze optimization. Long story short, this would be so much more complicated with worse result then just going back to what we know worked well and was more interesting, which is Kaiten.

Those 6 Kenki spenders are not that much in practice.
Kyuten is just AoE Shinten.
Guren is just AoE Senei. You use this only once every 2 minutes, with Kenki generated by Ikishoten.
Gyoten is gap closer, Yaten backstep, they're situational.

So realistically, you spend 90%+ Kenki on Shinten. Probably, I'm not doing the math, but even if it was 70% or similar, that's still way too much.

Senei with 1m CD wouldn't change much, look at the log I sent above, you do over 8 Shintens per minute and 0.5 Senei, so it will just be 7 and 1 instead. With pre-EW 50 Kenki Senei it would be slightly better with 6 and 1, but even that is still terrible.

As for Hagakure - that's possibly one of the most important SAM skills to make your rotation go smooth and makes SAM one of few jobs that can choose between 3 vastly different GCD speed, without any significant modifications to your rotation, I really don't know how did you find out it has no use.