This is actually one of the most often recommended approaches to solving this problem. If you're up for a bit of drywall work. You could cut open the wall a bit, and install the 2x4s between the studs.
For a quick fix, bolting 2x4s to the studs on the outside of the wall should work just fine. If you paint the 2x4s the same color as the wall, it might help to blend them in a bit.
Another option is to try and find a mount that accommodates 24" stud spacing, though this may not be an option if you already have a mount you want to use.
Do not use drywall anchors to hang a TV that large on a swivel mount. If it was a mount that didn't have motion, I might say that's acceptable, but not with a swivel mount.
You will need to use wood in some form to add the necessary strength.
Plywood can be attached to the wall studs using 3-1/2" lag bolts with fender washers. To provide a clean finish, the drywall can be cutout and the opening filled with the plywood. Then tape and mud the joints. Sand the surface smooth, prime, and paint. The plywood will be barely noticeable if done right. Be sure to match the plywood thickness to the drywall thickness.
If you do not want to remove any drywall, the plywood can be mounted directly over the drywall. You will need to use at least a 4" lag bolt in this case to account for the extra depth of the drywall. The plywood can be finished with a routed edge, sanded, primed, and painted for a finished look, if desired.
A final option for a truly hidden mount would be to open the wall by removing the drywall. Then install 2"x4" crossbracing between the studs at the correct locations for your TV mount. Replace the drywall, tape and mud the joints, sand, prime, and paint. The bracing is now hidden in the wall and you can attach the mount to the bracing.
Best Answer
TV wall mounts should always be mounted directly onto studs if the total weight is that much. If all mounting screws are going into studs, the drywall thickness is irrelevant. Drywall anchors are a great invention, but not suited for the kinds of load and forces a swivel wall mount exerts.
If you can't mount the wall mount onto studs for some reason (like, say, because the studs are spaced 24" and the mounting screws on the wall mount are <24" apart), mount a length of 2x4 lumber onto the wall and secure it onto the studs. Then mount your tv wall mount onto the 2x4. I suggest 2 strips - one for the upper and lower rows of mounting screws.
And of course read the instructions that come with the wall mount to see if they have specific recommendations for dealing with your situation.