TL;DR devs could copy/paste the illumination functionally of the light cantrip [albeit with smaller radius] into the produce flame cantrip without breaking any rules
the flame appears in your hand [does not say where so it could be on the back of the hand?] and does not harm the caster or the caster's equipment, thus there is no reason why the druid can not have the flame active while holding something, furthermore, while holding a bow you have a hand free unless you are activity nocking/drawing arrows so you have a hand all of the time out of combat and most of the time during combat, lastly at the very least you should be able to put the flamey thing in the light slot [where the torch/candle normally goes]
currently you have to disarm yourself just to get a small amount of light and the druid only gets two cantrips. so when the martials in the party are easily swapping out their torches for weapons they are snickering at the druid and making fun the nerdy treehugger
thus as is the produce flame is next to useless especially since they created the new longer ranged cantrip. at the very least allow it to work like the light cantrip when you pick the 'hold' option and arguably you might need a free hand to use the 'hurl' option
yellow flower of courage