Well.... maybe... but let's do the math and consider all factors. There is a lot more in the math than just assuming a service life and the cost per mile of that. There's financing, depreciation, etc... all of that plays into a potential future decision to sell/trade the truck down the line.
We'll have to make a couple of assumptions with interest rates, but that's not too difficult. Depreciation is a huge factor the first 4-5 years on a new vehicle but let's just look at the first 3 years. I assume that you're considering keeping the truck until it falls apart but I would mention that probably 90% of the population do not. So resale needs to be a consideration.
New truck cost: $52,400
1st year depreciation is ~20%: - $10,480. New value: $41,920
2nd year depreciation is ~15%: - $6,288. New value: $35,632
3rd year depreciation is ~10%: $3563. New value is: $32,069
Let's assume that you only drive around 1k miles a month. So, in 3 years (or 36 months) the truck has racked up 36k miles. Without even bringing financing into the equation, the truck has ACTUALLY cost
$1.77/mile solely based on depreciation.
Used truck cost: $37,000
By year 9, depreciation has slowed to roughly 3-5% per year (could be less).
10 year depreciation is ~5%: $35,150
11 year depreciation is ~ 5%: $33,392.50
12 year depreciation is ~ 5%: $31,723
Using the same driving assumptions above, the actual cost (just in terms of depreciation) is about
$0.14/mile. To add... the new truck will have lost roughly $20.3k in value over the course of 36 mos, whereas the used truck will lose roughly $5,200 in value.
Is having the bumper to bumper warranty worth the extra $15k?
Let's consider adding financing into the equation (72 mos loan, no down payment, 7% interest, 7% sales tax, $2,700 title/reg fees).
$52,400 - Total cost after repayment is $72,139.39
$37,000 - Total cost after repayment is $51,912.18
That's a difference of over $20k.
Is a new truck REALLY cheaper or are you simply paying a premium for the peace of mind?

If you never plan on selling or trading, it makes reasonable sense to buy new. But if you even have an inkling that you will want to upgrade again and plan to use the truck's remaining value towards the new one... you'll take a hit.