For context, the 737 NG is previous iteration of the 737 (before the MAX) and among the most popular aircraft ever built, with over 7000 in service. Grounding this would absolutely cripple the airline industry.
However, the NG also has an excellent safety record, and 35000 cycles is equivalent to 5 flights (takeoff & landing) every day for 10 years. So while this may lead to extra checks on older aircraft, it's highly unlikely to cause a MAX-style global grounding.
However, the NG also has an excellent safety record, and 35000 cycles is equivalent to 5 flights (takeoff & landing) every day for 10 years. So while this may lead to extra checks on older aircraft, it's highly unlikely to cause a MAX-style global grounding.