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Even with additional MCAS training the MAX could have retained a 737 type rating, but Boeing didn't even allude to the existence of the system in crew manuals, didn't program their simulators to accurately reflect the operation, and claimed they didn't expect MCAS to 'not operate under normal flight envelope conditions'. If that were true, though, of course, it would still be prudent to mention in the crew documentation that it exists.
There's more than one way Boeing could have implemented this system without losing the 737 type and while still remaining competitive to Airbus. Even Ryanair would choose 40 of MCAS-focused sim training to keep a consistent 737 fleet over splitting their pilot pool between entirely different aircraft, but I don't believe they even needed that. Just proper documentation and not giving the system priority over pilot input would have been enough. They could still have bribed/convinced the FAA to let them call it a flight control system under those conditions.