B737 MAX 8 flight crew reported on arrival at aircraft; a signed off discrepancy stating that the #1 engine auto shut down on start three times. The flight crew questioned the sign off and inspected the engine finding excessive coking present to the engine exhaust vent tubes. Maintenance acquired an engineering waiver to operate the aircraft and the flight crew departed. On a later flight; the Captain found excessive coking on another aircraft and that aircraft was removed from service. This led the Captain to question the validity of the previous aircraft's engineering waiver.

Narrative

Showed up to the aircraft for our departure from ZZZ ZZZ1. The logbook had an entry that said something to the effect that the number one motor difficult to start and auto shutdown three times. The corresponding fix was determined to be lack of airflow on the starter. I have over 13;000 hours on the 737 and I have never seen a write up such as that. So the copilot went to look closely at the aircraft on his preflight. The Copilot found the exhaust/vent tubes almost completely coked shut. Contract Maintenance came out and Company Maintenance sent him the limits on how much coking was acceptable. The coking was beyond Company Maintenance limits and Company Maintenance obtained an engineering waiver to operate plane with passengers for 3 days before cleaning required. I didn't think much more of it til today. I was given another MAX aircraft and it too was coked beyond limits and after I wrote it up Company Maintenance took the aircraft out of service. I was given another MAX and same coking issue where again I wrote it up and Company Maintenance took this aircraft out of service. I asked why not issue an engineering waiver and they said they couldn't. THAT is when I thought of our flight out of ZZZ with the engineering waiver. I'm not sure why these MAX airplanes are not receiving the required upkeep that would let them remain within coking limits. I could speculate I'm sure it revolves around money or mechanic availability but that is not my area of accountability. I'm only responsible for making sure my aircraft if in top working order and safe to fly to its intended destination. But with the now three MAX aircraft that I've seen with this issue I'm afraid the coking problem is a bit more widespread.