I wouldn't. The CT is rated by JD Power as THE most reliable car of all cars made. Put the $1900 in a savings account.
When I bought my used MINI I paid $2600 for a 3 year warranty and am very glad that I did. MINI has some of the worse reliability stats so that warranty looked like a bargain. I was in the black within six months.
here in the uk i purchased a 2 year extended warranty from lexus that included a 2 year AA pan european breakdown policy for £500 or $750 so for me it was a no brainer as it worked out at £125 or $187 per year for the warranty the rest is for the breakdown policy,here in the uk the lexus labour charge is £110 or $165 per hour so if i have just 1 incident then i have saved money.
You have to decide what "peace of mind" is worth to you, but I agree that it's not as easy as it sounds. I would be very tempted, based on the cost of repairs. If you don't choke on the initial cost, the peace of mind you get lasts 2 years and you forget about the cost. Assuming the warranty is a good one, it's pretty fun to walk away from an expensive repair that didn't actually cost YOU anything. Conversely, fighting with the warranty provider after paying for it would REALLY a irritate me!
But this is an exceptionally reliable car. I believe I would take the chance that it won't be breaking anytime soon, and save the money.
I'd only buy an extended warranty if they gave me a steal on the price. At $2k it's not worth it. That much money can be spent on a few repairs down the road. Now if they offered at $500 or less, then maybe...
I got the 5 year windshield warranty on my car because the dealer dropped the interest on my loan to where I save $80 for buying it
I also got an extended warranty that doubles my basic warranty on my Mustang because the dealer dropped the interest on my loan to where it cost me $150.
Well with the rate that intermediate shafts are failing on CT's. Out of warranty the dealer quote to replace was $1500. Considering that could be the only thing to ever go wrong then a $2k warranty isn't worth it.