No problem with Cook holding out - he's free to work, or not work as he desires.
Cook has already earned $4.6M. Playing this season on the existing contract earns him another $5.4M. He will have earned $10M before age 26. If you assume that between his agent and the tax man, he only nets half of that ($5M), he could have multi-generational wealth even if retired at the end of this upcoming season. If he controls his spending...
My issue is with your two implications:
First, that he needs this next contract to secure secure financial salvation for multiple generations. That the $10M in earnings on the first contract isn't enough for multi-generational wealth. Your second implication is that the difference between what the Bills would like to sign him to (probably around $10M/year) and what he wants, $15M/year) will be required for multi-generation wealth.
With respect to issue #1: Studies about NFL player bankruptcies show that larger contracts and longer careers do NOT substantially reduce their risk of bankruptcy in retirement. This study (https://www.bls.gov/opub/mlr/2015/beyond-bls/life-after-the-nfl.htm) projects 15%-40% of players, regardless of career duration and earnings, will file for bankruptcy within 25 years of retirement.
As to implication #2, I would bet Beane would gladly sign him to a contract for $10M/year for 2 years right now. I'm not advocating that Cook accept $10M/year, just making a point that he could likely sign a contract today that guaranteed him $20M over 2 years. That would get him a total of 30M in career earnings before age 28. He has indicated he wants $15M+ year. Over 2 years, that would be an additional $10M+ in earnings. So $40M in career earnings vs. $30M. I would postulate that if an athlete (or person) doesn't have the financial discipline to create generational wealth on $30M in career earnings, the bump from $30M to $40M won't make a difference in financial salvation.
Now, I don't have any issue with him (or anyone) holding out, refusing to play, holding in, etc. It's a free market. But let's not characterize this as "two generations of family wealth", or he's got to "feed his family" as Latrell Sprewell infamously said when rejecting a 3 year $21M contract 20 years ago. Speaking of Latrell, he had north of $100 million in career earnings and now has a net worth of about $150K. So much for financial salvation. Ronald Read, on the other hand never made more than minimum wage working as a janitor and gas station attendant yet died with a net worth of 8.6M
I postulate, above $500K in annual income, financial salvation is only dependent on your spending....