On $10k in taxes that's $250 (at 2.5%) to get one free night.
I don't follow your maths, but what I see for sure is you're not accounting for the value of HH points received. FNC is not everything. You should look at
my formulas and substitute 0.0086 for your HH valuation for a full picture, and then subtract the CC fee commission. (And for a complete result, also account for the value of CC fee spent as you earn HH on that too)
Here's how I'd approach this topic on Aspire card, which has a target of $30K for FNC#1 valued $621.68, assuming tax to be paid is $10K and commission is 1.82% (payusatax.com):
Aspire: (30000 × 3 × 0.0086 + 621.68 - 10000 × 0.0182) / 30000 = 0.040456 =
4% CB
$30K spent total, $10K of which requires paying a commission. Effective cashback is 4%.
Annual fee isn't part of the equation because AF on Aspire pays for itself with Hilton credits ($400), flight credits ($200), and more ($189 on Clear if you use it).
And entire $30K on federal taxes (specifically, $29463.76 on taxes, and the remaining $536.24 on CC commission):
Aspire: (30000 × 3 × 0.0086 + 621.68 - 30000 × 0.0182) / 30000 = 0.02832266667 =
2.8% CB
And an entire $45K on federal taxes for FNC#2 threshold on Hilton Business before 6/30:
BusinessFNC2: (45000 × 5 × 0.0086 + 621.68 − 45000 × 0.0182) / 45000 = 0.03861511111 =
3.9% CB
Aspire $30K per FNC, or Business $45K for FNC#2 (assuming you can make it) is still much better than using a generic 2.5% cashback card from Alliant where you're only making an effective cashback of 0.68%.
I can only reach Business FNC #1, not #2, so I'm going to pay with Aspire. Not my 2 Surpass cards, because I can reach their $15K thresholds with 6x grocery category.