No, for the same reason trucks aren’t overkill for horses in logistics. Unit costs, lead time, orbital flexibility: there isn’t a market for Ariane 6 left.
Even ArianeSpace’s CEO admits Ariane 6 is obsolete and that Europe needs “a reusable heavy launcher” [1].
[1] https://www.illdefined.space/arianespace-the-only-fish-in-th...
The biggest market is probably internally for Starlink. But itself, that'll be quite a lot of launches. Especially if SpaceX ends up pursuing an enlarged constellation size.
For the same reason, it's almost certain that ArianeSpace won't get any launches in the 2nd Kuiper tranche - New Glenn should be more efficient and capable than either Ariane 6 or Vulcan. Even if it isn't up to the task operationally, Vulcan will probably receive the balance of launches.