Thus, the interception goal would be to get them in their boost phase, or mid-course phase, rather than the terminal phase after they've launched the HGV (hypersonic glide vehicle). HGV phase, I think only laser/particle weapons would work given the time between detection and firing solution. But for mid-course, they could use SM-3/SM-6. The SM-3 is specifically designed for targets like the DF. So AEGIS systems with SM-3 might be effective in protecting US carriers as long as the launches are detected. The problem is, the HGV only spends a much shorter time in ballistic phase, and once it re-enters the atmosphere, it is no longer on a predictable ballistic trajectory.

That said, military tech often works much better in theory than in reality. The USSR/Russia had a fearsome military tech on paper, the evidence in Ukraine seems to be it was hyperbole.