For the first time in my life, I did so this past December using pay1040.com. They have the lowest % cost for credit card payments.
I did so even though I had plenty of money to pay myself. Bank of America was offering 3X on purchases on their Amtrak card. For example, doing a 10K payment would cost $187 and yield 30,000 Amtrak points. Amtrak points are worth 2.6 cents each on typical non-Acela travel. For example, I booked a trip with my child for a sleeper from lower Florida to upstate NY for 20k points, which would be (2/3*)*187 = $125. So for $125 in fees I got enough points for a sleeper for 2 people which includes 6 meals (3 per person), and I paid taxes in 2018 w/o having to pay until early February 2019.
As I stated, this was a first time for me and even with working the numbers I was hesitant...
ETA: Of course, there was more to my analysis. For instance, had I purchased the train using my credit card (BOA Amtrak), I would have spent $520, but would have gotten 1560 Amtrak points from the purchase.
ETA 2: Forgot to mention the $10K spend also got me Amtrak Select status. Which brings up the consideration that this technique might be good IF you are trying to reach a minimum spend or other special deal on the card being used.