I don't really see it as punishment. They can either accept the new system of cash flow that doesn't pay as much or go find another job.
Here's how I see it. Owners should fund new stadiums themselves. If the issue is that it's too expensive even for them and the profits they are making, then the players and coaches should start being offered less money. It makes sense, because in this type of system the owners aren't making as much profit because they are paying for new stadiums to be constructed every 20 years.
You have the economics completely bass-ackward, and I'm not sure whether you're doing it intentionally (I'm leaning toward "yes").
The market supports current advertising rates for NFL games, current ticket prices, current prices on TV and streaming services, and current prices on merchandise. For NFL teams to charge any less than what they can would be business malpractice, and their MBAs would never let them do it.
Given that there's market support for the current billions of dollars in revenue, I want as much of that as possible to go to the players. It's the players we want to watch. It's the players who push the limits of human performance in this specific game. What the owners have to contribute is money, and money by definition is fungible. There's a line around the block of billionaires waiting for the opportunity to buy a top-league professional sports franchise.
The choice isn't cheaper NFL experiences vs. the players being fairly compensated for being among the top 2% of the top 1% of the top 1% of the top 1% in the world at what they do, in an industry where their work generates many billions of dollars of revenue. The choice is between the players being fairly compensated on the one hand and the owners simply pocketing more of the revenue they've already discovered the market supports.
The owners and their buddies in the media like to keep spreading the
zombie lie that NFL prices are high because player salaries are high. The truth is exactly the opposite. The owners hire people to keep their prices where they optimize profit, and so far, that has meant prices climbing consistently, with no signs of slowing down. The players negotiate a percentage of league revenue to be spent on player compensation. So it's not that NFL merchandise, ticket, and subscription prices are high because the poor owners need the money to pay the players. It's that the players have correctly demanded a significant percentage of league revenues for player compensation and the greedy owners won't stop jacking up the prices, so
player salaries are high because the prices are high [EXACTLY THE OPPOSITE of the zombie lie you're helping to propagate by suggesting that cutting player salaries would somehow make NFL experiences cheaper], and the prices are high because the teams have found so far that the market is willing to pay those prices.