You don't need steel core to burn through steel plate. My .270 with 90grn HP did a number on my walking targets...
Most high-velocity full-power rifle rounds with military FMJ or civilian hunting bullets will punch through steel plates without much trouble. Some bullets specifically designed for target shooting lack the structural integrity to do the job, but these bullets are the exception, not the rule.
The legal issue is with low-velocity handgun
bullets; refer to sigcurious' prior post.