what is the problem?

yes

I think that perhaps the word "clever" is a little strong for this particular piece of wordplay, unless there is some regional variation. in UK English "clever" means "intelligent", "witty", "ingenious", etc.

Maybe 'cute' then.

I have to admit I haven't penetrated the intended meaning of the tag line, so only guessing.

I think it may miss its target as far as native speakers are concerned, especially considering one meaning of "love egg" in the West. Or maybe that is part of the pun, although I somehow doubt it.

One thing I have noticed in countries where English is not the native language, is a tendency to use English words and names in order to be "cool" or "cute" in a way which is sometimes jarring to a native speaker. It seems as if English is cool, and people seem to just pick words out of dictionaries or employ word-for-word translations of the Babelfish type. I don't mean the well known things like menus which include "squid boiled in his own ink". I have seen a bar in Nice called "Charles Dicken's" and one in Norway called "Sherlock Holme's".

I wonder if the notice originally referred to is an example of “wasei eigo” (Japanese-made English).

There is a phenomenon called Engrish:

I was being kind.

From the context you describe, I take it you were in Japan? Your foreign friend most likely would have expected, "We love eggs." I'm in South Korea, and in Korean language, plurals are not used unless there is a strong reason to. When they translate something into English, they tend to use the singular form. For example, a sign above a toilet entrance usually reads "Man" or "Woman" instead of "Men" and "Women." Native English speakers would use the plural forms. I only had one semester of Japanese language, and that was years ago. I seem to recall that most nouns don't even have a plural form. Is that correct?