The Federation and its Starfleet do believe in battleships; it's just unclear whether this is an exclusively foreign type of ship, or also part of the Starfleet arsenal. They also believe in battlecruisers (and the Klingons liken Kirk's ship to one); in heavy and light cruisers, frigates and destroyers (and Starfleet possesses examples of each, even if the latter two are not unambiguously associated with any design); and in certain futuristic types such as explorers.
None of this helps much in defining what the TOS Starfleet had or didn't have. We saw extremely little of that organization, and many interpretations of our necessarily biased view can accommodate ships much bigger than Kirk's, a fleet of thousands, a great number of Vulcan ringships, whatever the greater story needs.
Now the greater story is DSC. Can any interpretation accommodate a large number of ships different in design from the ones seen so far in other spinoffs? I don't see any difficulty as such: DSC is already guaranteed to give us the distinct Shenzhou and Discovery aesthetics side by side, no different from the TNG era having a number of styles (some of which we eventually learned were "older" or "newer", and DSC isn't letting us do that quite yet). Older designs have disappeared without explanation before, so there's no problem with ENT or Kelvin styles being absent, either; as always, the rationale is left as an exercise to the audience.
Timo Saloniemi
None of this helps much in defining what the TOS Starfleet had or didn't have. We saw extremely little of that organization, and many interpretations of our necessarily biased view can accommodate ships much bigger than Kirk's, a fleet of thousands, a great number of Vulcan ringships, whatever the greater story needs.
Now the greater story is DSC. Can any interpretation accommodate a large number of ships different in design from the ones seen so far in other spinoffs? I don't see any difficulty as such: DSC is already guaranteed to give us the distinct Shenzhou and Discovery aesthetics side by side, no different from the TNG era having a number of styles (some of which we eventually learned were "older" or "newer", and DSC isn't letting us do that quite yet). Older designs have disappeared without explanation before, so there's no problem with ENT or Kelvin styles being absent, either; as always, the rationale is left as an exercise to the audience.
Timo Saloniemi