First, Zoom now refers to live captioning as live transcription. Second, Zoom has said that all accounts including free accounts will have access to live transcription by fall of 2021 (fall in the northern hemisphere). But in the meantime Zoom will provide live transcription for free to all meeting hosts who need it for accessibility reasons. Zoom requests that you fill out this form to request live transcription be turned on in your free Zoom account.
Zoom's complete, updated statement about the availability of live transcription can be read here.