Hi Adam Young we recommend to keep transcripts on to help viewers engage better with video, and because this same data also powers captions for accessibility. If this doesn't work for your particular needs, the teams live transcript feature is off by default for a tenant so that the meeting recording transcript isn't captured unless an admin turns that policy on. And for Stream on SharePoint where the features are on by default, transcript generation can be turned off either globally for the tenant (Set-SPOTenant (SharePointOnlinePowerShell) | Microsoft Docs) or per a SharePoint site level Set-SPOSite (SharePointOnlinePowerShell) | Microsoft Docs (which can also be applied at the level of an individual's OneDrive for Business account).
To clarify one point, transcripts stay within your organization and are handled the same way your organization manages any other office document (word, PPT, excel) stored on SharePoint or OneDrive for Business.
We are continually improving the accuracy of transcripts to better capture what was said and you're correct that they're not 100% accurate. For the cases where 100% accuracy is required, users can edit for accuracy as described in this article and we're also working on new ways to make that easier!