Not necessarily. There are a lot of factors that will go into the PS6 price--chiefly what it actually costs Sony to manufacture come 2027 or 2028 which is presumably when the PS6 will release.
We also need to bear in mind that the PS5 Pro is a niche product. PS6 will be a mainline, tentpole product. It's going to be priced to move. If necessary, Sony will subsidize it to an extent--though we won't see the kind of disastrous subsidy levels that the PS3 incurred, that's for sure.
People still need to calm down over the price of the PS5 Pro. It's not a mainstream product. We know this from experience. The PS4 Pro was much more affordable, and still made up very little of the PS4's install base, only about 10%. Most PS4 gamers did not upgrade to the Pro, and gamers new to PS4 largely opted for the cheaper base model over the Pro.
The install base for the PS5 Pro will in all likelihood be significantly lower than 10% and largely limited to professional gamers, content creators, and videophiles. You can call Sony greedy or arrogant all you like, but don't think they're stupid. They've created a very high end PS5 option for a small, niche portion of their market. Knowing its sales will be small, they won't be flooding the market with tens of millions of PS5 Pros, and they absolutely are not subsidizing it because mid-gen refreshes do not drive up software and subscription sales like a new generation does. The hardware is profitable at the initial point of sale.
We've no real idea what a PS6 will theoretically cost. In 3 to 4 years, $700 in today's money could be much closer to $1000 if the economy continues on its current trajectory. As it is today, the $599.99 price point of the PS3 at launch in 2006 is $936.88 in today's money. That puts the PS5 Pro very notably cheaper than the PS3 was eighteen years ago.