The two things that should keep Alaska independent are that Alaska's market cap is so high, making the purchase expensive, and that purchases of a West Coast airline have ended badly each time they've been tried.

US Air bought PSA - and there's nothing left.
AA bought AirCal. Having not learned anything, they later bought Reno Air. There's nothing left of either of them.
DL, considered experts at acquisition, bought Western. They kept the SLC hub but lost most north-south flying along the coast. Western once connected LA-SF-SEA and went up to Alaska.

That's not to say that some airline management won't some day decide to try again, but it's hard to see that either AA or US could afford Alaska, nor that the system would be a great fir for either of them. It might be a better fit for Delta.

How about JetBlue or VX? The fleets are incompatible, and there doesn't seem to be much synergy. Spirit? Sure hope not. Frontier? Maybe that's the best option. Of course they are also an A319/320 airline tied with a lot of Republic RJ flying. Maybe there's something to be done. A marger with Hawaiian isn't as attractive and would make them too dependent on that market.

The other reasons that airlines have been acquired is to get a lot of aircraft quickly, or to get gates or slots. This doesn't seem a time when anyone needs to acquire aircraft, and Alaska doesn't really have much in the way of slot or gate assets at congested airports.

On the whole, there isn't a strong case for anyone to acquire Alaska, so maybe Bill Ayer is just stating the obvious.