OP - You've answered your own question. Carriers can charge off the charts fares for F because some, albeit very few, are willing to pay it. Why would they sell someone like you a seat for $1,500 when you are willing to pay $2,000?

Unfortunately, your comparison of fares is applies and oranges. The likely coach fare you quoted at $200 is almost certainly deeply discounted non-refundable and non-changeable. The same fare in Y (full fare coach which can be changed and cancelled for a full cash refund) is most likely $1,000, approx 10x the deepest discount. In that light, full F (which is fully refundable & changeable) isn't that much more. The more flexible your fare is, the more it will cost.

Other things to consider, if you can live with non-changeable / non-refundable are Y-UP fares where you pay the full Y and space available are assigned a seat in F at the time of booking. The carrier can tell you at the time you book whether this is doable. You will have to do the research and your best bet since you seem unfamiliar with the system is to actually call and pay the phone reservation fee.

Those on FT who talk about the lack of value in F fares may not have a basis for comparison. Whether a seat is worth $2,800 more in F than in Y is a matter only you as an individual can determine. Can you afford the higher fare? What will you give up to be able to pay the higher fare? If it's feeding your kids, don't fly F. If you have the money, sure -- do it.