FL law went into effect last October that you do indeed need to possess a valid DL when on public streets. Also under 18 must have a valid learners permit or valid DL. Yes you will can/will get a DUI or open container violation on a golf cart. Speeding is also an issue and some people are finding out their 30 mph cart will get them in trouble.
Interesting since many older seniors here no longer have DL licenses, but still drive golf carts. I know they’re okay on the multi-modal paths, but sometimes have to go on the street in the diamond lane where there’s no MMP.