A few reasons
First, the short one. The US spent a bunch of time in the pre-war period playing with a .28 cal bullet in the form of .276 Pederson and were left somewhat unimpressed, especially by its comparatively lackluster barrier penetration which was a large preoccupation in American cartridge thinking.
Second, the island hopping campaign in WW2 left a very serious impression on US logistics officers. Go read about any little 300 man battle on any little stoop of an island and you'll find a story about the unbelievable difficulty of doing anything. War is an environment where everything goes wrong all the time and even by that standard, conducting and supplying an opposed naval landing is about the hardest thing you can do. It was made harder than it needed to be by the US's wide variety of ammunition forms. The US issued:
>30.06 in clips for the Garand
>30.06 in belts for the M1919
>30.06 in magazines for the BAR
>.30 carbine in magazines for the M1 carbine
>.45 ACP in magazines for the Thompson (and later the M3 with its incompatible mags)
This is just for small arms, and every company needed the correct mix of this delivered right to the beach, prepacked and ready to go on a regular schedule, in addition to every other consumable of which there were dozens. US logistics officers spent the war desperately trying to dream up a way to eliminate even just one of these forms and failed. Entering the postwar period, the slowly materializing threat of a land war against the Soviet Union and the sheer amount of material the US would have to shovel into western Europe to save it and the speed with which it would have to be done made the invasion of Okinawa look like a joke. This is why the US was so highly motivated to choose a single cartridge that could do everything and a single rifle to go with it. In the FG-42, they thought they found their answer. A (nearly) handy rifle chambered in a full power cartridge that's (nearly) controllable in full-auto? What a godsend, it could replace everything except maybe the belt-fed. Early prototypes of what would become the M14 strongly resembled the FG-42, with a straight line stock and elaborate muzzle device (see attached).
Third, .280 British went through a bunch of changes. Going into the program, the US's only demand was that the bullet had to have a steel core because by that point they had a few decades of reports pointing with increasing certainty at the fact that the US did not have enough lead reserves or production to be able to supply a major land war with a lead-cored bullet. Early .280 British was lead-cored. It was changed to steel at the US's insistence, but the steel cores were seated inconsistently and reportedly had accuracy as bad as 12 MOA. The British recruited the Belgians to help them unfuck it, and after some doing they brought it down to 5-6 MOA which was sufficient to meet minimum requirements. Now that the mere technical problems had been mostly solved, they ran into the conceptual ones.
If you're going to standardize on a single infantry cartridge, before all else it needs to be a good machine gun cartridge. Infantry combat revolves around the machine gun. In WW2 and Korea machine guns consistently inflicted ~80% of the casualties done by small arms in total. US ordnance had clear ideas of what a machine gun ought to be, and the ability to efficiently chew up light cover was one they rated highly. 30.06 M2 AP was in American minds the gold standard for "fuck you and everything you're hiding behind" (and still is, it's the reference threat for level 4 armor). .280 British didn't quite measure up in any of its incarnations.
There was a bunch of infighting and political skullduggery going on as well, with the US Ordnance Dept's old guard quite certain that the best gun that could ever exist was a mildly modified M1 Garand chambered for a mildly modified 30.06 M2 and younger thinkers quite a bit less sure. I'm not entirely sure which side department head Col. Renee Studler was on (the one single faggot >>9203
mentions), popular history lays most of the weight on his shoulders but the earliest SCHV studies conducted by the US army thank Studler by name for his patronage. In any case, Studler retired at the critical moment in 1953, the empowered old guard took the opportunity to flush their rivals and got their granddad gun and its granddad cartridge, and the Ordnance Department and Springfield Armory ultimately died for it.