The price has already gone about 100% in about 12 years.. (much faster than inflation -- the inflation rate is about 20% over the decade... so the pricing of the DDP has risen 5 times faster than inflation).
It's not a question of whether it's profitable. It's a question of whether there are better ways for MORE profit. No, not raising the price -- the DDP has gotten less popular overall, as more people realize it's cheaper to dine without it.
In 2007, the dining plan cost $39, it included appetizer AND dessert at TS and CS meals. Most critically, it INCLUDED gratuity.
Each year, they have tinkered with the dining plan.. increasing prices. Taking away benefits. Then adding limited benefits that create a perceived savings but really just increase profit for Disney. (Including alcoholic beverages costs Disney very little but greatly enhances the perceived value for some guests, for example... but cutting out gratuities was a huge cost savings for Disney -- Disney would much rather give adults the option of a glass of wine than pay everyone's gratuities).
But as I said -- as it is designed, the DDP limits restaurant flexibility of menu design and dining concept. And with each incarnation, the audience for the DDP gets smaller and smaller.
I suspect it will be a good time for them to go back to the drawing board -- to create dining plans that allow greater flexibility and can appeal to more guests.