As a non economist let me explain:
80% (I’m being generous here, it’s probably closer to 90%) of all transactions happen in Everfall or Windsward.
That’s means 80% of the undercutting and deflation is already happening right now.
The 20% of sales from other areas are mostly by flippers or people who only harvest to sell at the lower volume higher prices and those higher prices are paid by the 20% who are too lazy to travel for lower prices or unaware (noobs) that prices are lower elsewhere.
After trading posts are linked you add in the 20% customers who were paying the higher prices and now don’t have to. They may actually buy more now that they are exposed to lower prices.
The 20% of higher priced product that was purchased prior will be equalized into the market but so were the customers.
If people were specifically gathering only because of selling for the higher outlying price, and they stop their gathering because unwilling to do the work of gathering for the lower (Everfall) prices they won’t be contributing to the goods market anymore, but the customers will still be around and part of the linked in market.
Whatever the numbers are the day before linking, a server will have the same number of customers and gatherers after.
*statistics made up for purposes of illustration. Your server may vary
Side note: After the linking towns will have to compete for lowest taxes and fees to try to become the new sales “hub”, rather than just jacking up taxes and fees in the 2 most popular cities because everyone had to go there to get deals.
Having upgraded crafting stations will be a draw too, of course.
I’m looking forward to the convenience of just listing and buying from wherever I am rather than dragging full inventories around, but if taxes and fees and stations become really good and it looks to be ongoing, I’d move.