What does the Greek proverb “nothing done with intelligence is done without speech” emphasize? And how to interpret it culturally?

I don’t have the answer, but this will help narrow it down:

This is not a proverb as such, but is a quotation from a speech by the orator Isocrates. Nicocles, section 9:

οὐδὲν τῶν φρονίμως πραττομένων εὑρήσομεν ἀλόγως γιγνόμενον

The emphasis out of context is not quite as obvious, because the same word logos is used to mean “the faculty of speech”, “a speech”, and “reason”. In fact the word alogōs normally means not “without speech”, but “irrationally”. But in context, Isocrates is extolling speech as the faculty that both distinguishes us from animals, and that lets us pursue social interaction (including oratory). And ultimately, he is saying that  people who speak for a living (like orators) are pursuing a noble profession:

Nicocles or the Cyprians, 6-9:

But, because there has been implanted in us the power to persuade each other and to make clear to each other whatever we desire, not only have we escaped the life of wild beasts, but we have come together and founded cities and made laws and invented arts; and, generally speaking, there is no institution devised by man which the power of speech has not helped us to establish

For this it is which has laid down laws concerning things just and unjust, and things base and honorable; and if it were not for these ordinances we should not be able to live with one another. It is by this also that we confute the bad and extol the good. Through this we educate the ignorant and appraise the wise; for the power to speak well is taken as the surest index of a sound understanding, and discourse which is true and lawful and just is the outward image of a good and faithful soul.

With this faculty we both contend against others on matters which are open to dispute and seek light for ourselves on things which are unknown; for the same arguments which we use in persuading others when we speak in public, we employ also when we deliberate in our own thoughts; and, while we call eloquent those who are able to speak before a crowd, we regard as sage those who most skilfully debate their problems in their own minds.

And, if there is need to speak in brief summary of this power, we shall find that none of the things which are done with intelligence take place without the help of speech, but that in all our actions as well as in all our thoughts speech is our guide, and is most employed by those who have the most wisdom. Therefore, those who dare to speak with disrespect of educators and teachers of philosophy deserve our opprobrium no less than those who profane the sanctuaries of the gods.