I guess another way of looking at this is by asking, what can I do with a .240 that I can't do with a .243? Sure the .240 has a higher muzzle velocity, but any difference in trajectory is easily compensated for by a few clicks on the elevation turret since the force of gravity is known and unchanging, whereas compensating for wind drift tends to be the one that gets us in trouble. I'd expect a benefit from having a bit more velocity combined with a slippery bullet to reduce the time of flight to the target. If the .240's advantage over the .243 is 200 fps at the muzzle, shooting a slippery bullet like Hornady's 103 gr ELD-X, sighted 2" high at 100 provides a 250 yard zero. At 300 yards the .240 has a 1.8" advantage over the .243 loaded with that same bullet, or about 2 quarter minute clicks on the elevation turret. Again at 300, the .240 has about a half inch windage advantage over the .243 in a full value 10 mph cross wind. The typical quarter minute windage adjustment found on most scopes isn't fine enough to dial in the adjustment.
So if the advantage at 300 yards is mostly theoretical, what about at 500 yards? At 500 yards the difference in drop favors the .240 by 6.6" so an additional 6 clicks of elevation gets us close. Between the two cartridges, we have a 1.6" advantage in windage, again assuming a 10 mph full value cross wind, favoring the .240. A single click of windage adjustment isn't quite enough but 2 clicks is a bit too much, so holding off might be a better solution, particularly if your scope has a long range reticle. So if you still think the .240's advantage over the .243 is one you can exploit in the field, it might be worth the effort, but on a cost vs reward basis, now that I've looked at the numbers, I don't see it, and I doubt the coyote could tell the difference.
If starting from scratch I get the logic behind choosing the .240. For one thing, when long slippery bullets are loaded so the cartridge can be fed from the magazine, the long cartridge's powder capacity is less likely to be impacted than the shorter cartridge's, the degree of which is determined by the bullet and powder selection, and the magazine length of your particular rifle. Since you've already bracketed the .240's performance with a .243 and a .25-06, perhaps you just want a collection of rifles that perform very similarly, and if so, there is nothing wrong with that.