There are rules in place to prevent this type of thing, or at least make it financially non-viable.
https://www.sportingnews.com/us/nfl/news/nfl-franchise-tag-meaning-deadlines-values-rules/1o185fk9ywga31hax6m1ahgn3q#:~:text=Players can be tagged in,of the player's previous salary.
Players can be tagged in consecutive years, but the team must pay the player more each year he is tagged. (Kirk Cousins can tell you all about it.) For a player to be franchise tagged two straight years, the team must pay 120 percent of the player's previous salary. If it's three straight years, the team would need to pay the player 144 percent of his previous salary.
From the CBA: Any club that designates a player as a franchise player for the third time shall, on the date the third such designation is made, be deemed to have tendered the player a one-year NFL player contract for the greater of ...
— (A) the average of the five largest prior year salaries for players at the position with the highest such average
— (B) 120 percent of the average of the five largest prior year salaries for players at the position at which the player participated in the most plays during the prior league year
— or (C) 144 percent of his prior year salary.
If the club designates the player as a franchise player for the third time, the designating club shall be the only club with which the player may negotiate or sign a player contract.