Actually not, Asvel can reach level 10. In chapter 5 you also don't need rely on Asvel to kill numerous enemies, but Nanna that used speed-ring and live-ring.If Asvel killed the three enemies, 2 bishops, boss, dark bishop, dark marg, and Sniper, you reach level 8 or 9 without paragon mode. So if it's paragon mode you must reach level 10. If not, in chapter 6 Asvel kill some enemy at 1st turn and reach level 10 definitely, and you can clear at 7th turn in that way.
I don't like relying on Asvel in chapter 5, since Evel also has the reset possibility. Well, it ends in 15 turns so doesn't make any difference, though.