Is there another way of saying “less is more" in the following context?
They changed their packaging and left only the essential branding on it. It epitomizes "less is more".
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To quote a US president, "that depends on what the meaning of 'is' is."
This phrase implies a subject and verb (via the equivocal "is") of some cause, as well as the resultant effect. At times, explicitly stating an idea is preferable to implying what the result might be (more brand recognition? more market share of the target demographic?). I would suggest that the critical idea is that simplicity (or minimalism, as @GetzelR notes) will achieve a greater impact (e.g. sales revenue).
In this context, an alternate way of stating the key phrase is to explicitly say that "a simpler package design might appeal to more customers, thus creating higher sales revenues for the company." However, by specifying both cause and effect, one finds oneself wielding a longer sentence containing some information that the target audience already understood (of course they're selling more!), supporting the idea that, well, sometimes "less is more."