Both the corbins, Dave/corbins.com and Richard, rceco.com, address this in their writings. No big deal. You have to anneal the cases for better results. Most of the heavy press handgun bullet dies can do the final forming. Swage to best diameter. Ch4d.com? Corbin? Corbin? Blackmon? Hollywood? Well annealed the brass is little harder than the copper jackets. Slight greater tendency to be brittle and shatter.
As suggested, the .22 rimfire case has been used for decades. Basis of the firms Hornady and Speer (once, briefly, partners I am told). Sisk? Donaldson wrote of making his own bullets out of "short" cases.
.223 is .375 approx. Ideas. .45 ACP can be formed into rifle bullets or very heavy handgun bullets. Now with the .475's and .500's even more useful. '06 and .308 are .473... but very heavy brass in the base.
Mr. Corbin(s), both, have writings posted on web site for free review, download, study... read up and pursue if it suits you. Happy trails.