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I suppose both readings are grammatically defensible, but the context suggests the authors mean “often/a lot of” rather then “well”.
“Eating well” implies either a healthy, balanced diet or having sufficient food so as not to starve. Neither really fits the context - rice will not help you much if you lack micronutrients, and there is no mention of starving or food shortage before the times of rice mixing in the text.
Rather, reading よく as “often/a lot of” ties in with the previous sentence discussing the huge popularity of sushi with the Japanese - our sentence can be read as an explanation for it.
I would even be tempted to read すし as the main subject of our sentence, carried over from the previous one:
おすしは、子供達からお年寄りまで、たくさん人に人気の日本の食べものです。
Sushi is a Japanese food that is popular with a lot of people, young and old.すを混ぜるとご飯が長持ちするので、むかしからよく食べられてきました。
It [=sushi] has been eaten often since the olden days because rice, when mixed with vinegar, doesn’t spoil easily.
Note: sushi is prepared with rice mixed with vinegar, sugar, salt and other stuff [link]