A 223 will do anything a 22-250 will do and more. One can get a 223 in a faster twist barrel to allow shooting heavier bullets, as mentioned surplus ammunition, cheaper ammunition, the use of thicker military brass if you reload, and more ballistic data.
Hoosier
And if you think you need more range, why not get a 220 swift, .243, or a 25-06, or a 7mm mag, etc.
Hornady Reloading manual
223 Remington Max loads
45 grain bullet will make 3600 fps with 2 powders.
22-250 will do that with every powder listed.
223
50 grain bullet, 3400 fps with 6 powders out of 10 listed.
22-250 will pust that 3600fps with every powder listed and make it to 3800fps with 7 out of 10 powders listed and 3900 fps with three powders.
It only get's more obvious as the bullet weight increases.
223, 60 grain bullet, 3200 fps
22-250. 60 graom bullet, 3600fps
If those numbers sound the same to you then I guess "A 223 will do anything a 22-250 will do and more".