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The first carriers were battleships WITHOUT their fighting superstructure. No?

No.

The Lexington and Saratoga were converted from incomplete battlecruiser (CC) hulls, after the class was cancelled under the terms of the Naval Treaty. Battlecruisers were big-gun ships that sacrificed the armor of Battleships for speed. Great in concept, but between Jutland and HMS Hood seen as not so good in practice.

The Lexingtons' speed as CVs was the same as it would have been had they been completed as intended as CCs.

The pre-WWII "fast battleship" classes of North Carolina and South Dakotas had top speeds in the high-20 knots. They could not keep up with the CVs at flank speed, but the CVs rarely operated (at least continuously) at flank. So despite their "slower" speed the six BBs of those two classes ended up performing yeoman service as anti-aircraft escorts for the fleet carriers.

Even during the "Battle of Bull's Run" during Leyte Gulf, when Halsey went charging off after the Japanese decoy carriers, he kept the "slower" fast-BBs with him. The result was the famous "WHERE IS RPT WHERE IS TASK FORCE THIRTY FOUR RR THE WORLD WONDERS" message from Nimitz, wondering where TF34, centered on the Battleships Washington, Alabama, Iowa and New Jersey, was.