Qualified long-term. My first company didn't allow us to transact until long-term. My current does. However I think I disagree with you semantically on saying ESPPs are regulated by companies. They are regulated by various government regulations that a company must follow for it to be a qualified plan and there is a total cap of $25k of total value for example. Companies can determine many of the provisions though. But I think that's what you were probably saying.
My current company had a 2 year offering with quarterly purchases and full look back to the beginning price on any purchase with a rollover if a new offering had a better price. About the best I've ever heard of. Having your price locked in for 2 years and only having cash withheld for 3 months before purchase is pretty nice.