We've only done two cruises but we've booked our airfare separately on both occasions more for the flexibility of it but also for some savings. We've had success so far.

Our first cruise, we landed in Miami a few days early so we could check it out (first time to Miami). On the return, we stayed one more day in Miami so there wasn't any issues missing the flight. Getting off the ship took forever though because we indicated on our cruise info that we didn't have get off quick due to an early flight.

For our second cruise, we risked it a bit and flew to LA the day of. We drove from to Bellingham and flew to Long Beach airport (via Seattle) instead of LAX. We were able to fly to Long Beach which is way less busy and way closer to the cruise terminal than LAX. We like to try to get on the ship as early as possible so we took early flights. However, we also confirmed that if one of our flights/connections got canceled or delayed, there were other flights that would have gotten us to Long Beach with enough time before they closed boarding.
On the way back, we carried our own luggage off so we were one of the early groups off the ship. Got to LAX for a flight back to LAS way early.
In the end, we flew (1) BLI to LGB via SEA and (2) LAX to LAS and (3) LAS to YVR which was still about $200 or so cheaper (combined for the two of us) than the air/cruise package for YVR to LAX return that travel agency (whom we only bought the cruise from) was offering.

If you are concerned about missing the cruise or flight because of delays:
On the way there, a common suggestion is to fly in the day before.
On the way back, if you want to be safe, pick a late afternoon flight. The cruise also lets people off in groups based on their departure flights. Alternatively, pick a late evening flight and do a post cruise tour with the ship.