Per the Google: Maximum age at time of application is 31 for the FAA. Mandatory retirement age (from actively working traffic) is 56. Training is 2-5 months in Oklahoma City, then 1-3 years OJT before being fully certified.
https://www.faa.gov/be-atc#
That gives a max age candidate 25 years working traffic, minus training time, so more realistically 22 or 23. I somewhat understand the logic, if someone was 45 and was hired, minus training time, that might mean an eight year "career" working traffic. Not sure what all that training costs, but it can't be cheap. You could move on to management or training or another non-traffic job within the FAA, but you can't work traffic after 56. Like the mandatory retirement age for pilots, people smarter than I can debate whether that's the right age, but that's the current rule.
There is "with limited exceptions" behind that maximum hiring age so maybe someone separating from active duty at age 31.5 could get in? I would think the FAA would welcome veterans with appropriate experience with open arms, regardless of whether they're 30 or 35.
Blaming the PATCO strike that happened over 40 years ago is a bit disingenuous, that ship sailed a long time ago. The NYT can bring it up (column-inches to fill?), but Congress and the FAA have only themselves to blame for the current situation. It's not like the staffing issues in places like NYC and Florida aren't well-known and have been for years.