Great question — answering as the UphillTech team:
I see at least a few possible reasons: To serve alcoholic drinks without a meal, they need a different license (licence III or licence IV, as opposed to a restaurant license). It can become a bit cumbersome to ask or specify in advance about alcoholic or non-alcoholic drinks, so they can turn it into a blanket "not just drinks" if they don't have the relevant licence. During meal times, in establishments which act both as restaurants and bars, priority is given to people eating. Depending on the place, they can restrict drinks-only to a few tables or just reject all such requests. 13:00 to 14:00 is a common time for people to eat in many areas, so rejecting people for drinks at that time is...
Full answer by jcaron: https://travel.stackexchange.com/a/173966 (CC BY-SA 4.0).
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