For the average person, no. Long answer, it depends.
Only travel a few times a year? Plan trips in advance? Loyalty is NOT worth it. Go with the cheapest ticket and opt for a flexible points card (not a specific airline card).
If you travel a lot for business and are often booking last-minute flights, loyalty is worth it.
You'll have a reasonable chance at achieving elite status.
When booking last-minute, using your miles can be cheaper than the market fare.
I fall into the first category, so I always go with lowest fare.
My strategy is to build airline miles across the three major US carriers that have international reach: American, Delta and United. I redeem miles for international travel, thus prefer to consolidate miles with partners that have international routes and alliances. There's usually a lowest fare among one of these three, and by having a base of miles in each account you can take advantage of the routes where they have lower-than-average award travel redemptions as opposed to being stuck with one airline's rewards program. Finally, since airlines have elite status challenges and matching programs, you can still manage elite status without being loyal to just one airline.