About 10 years ago, I used to think people were crazy spending more than $1000 on a bicycle but bikes were not a hobby for me then.
Like most hobbies, prolonged exposure reduces sticker shock.
Nowadays my threshold is $3000 for a casual rider, which you are not.
If I rode as much as you do, I wouldn't hesitate to spend $3K on a bike.
200 miles a week is more than many peoples' commute to work.
That amount of mileage deserves a better bike.
Compared to racing cars, you'll get far more use out of a bicycle than a few sets of car tires or racing fuel.
If you can afford it, buy as ridiculous a bike as you can justify, or buy 2 different types to spread your money around.
When you get to $3K my head starts to think titanium bike.

I barely ride at all, but I'll probably buy a $2-3K road bike just because I don't want to put my money anywhere else.
Sometimes I think about getting a Moulton just to hang on a wall as art.
I know I wouldn't be faster than on a $500 bike, but I would enjoy a more expensive bike because I can feel a weight savings and I think it is a more refined system.

After you do some more research on which bike is best for you, I say go for it