No it could not just fly fine, it is to comply with regulations regarding stick forces when approaching stalls. Putting it on a new type certificate would have meant that all the old designs and solutions that today are grandfathered in by being used for decades safely would have to be updated to modern standards while also losing all advantages of the large amount of certified pilots.

MCAS is a longitudinal stability enhancement. It is not for stall prevention (although indirectly it helps) or to make the MAX handle like the NG (although it does); it was introduced to counteract the non-linear lift generated by the LEAP-1B engine nacelles at high AoA and give a steady increase in stick force as the stall is approached as required by regulation

http://www.b737.org.uk/mcas.htm