Does an abundance of supplication in prayer—such as supplicating in every prostration and in all prayers—harm it, based on the saying of some shaykhs that prayer was not legislated solely for supplication?

There is no harm in supplicating extensively and prolonging prostration for one who is not an Imam; rather, it is recommended, due to the Prophet (peace and blessings be upon him) saying: "The closest a servant is to his Lord is while he is prostrating, so increase in supplication." The Prophet (peace and blessings be upon him) once prolonged prostration to the extent that it was nearly as long as his standing. As for the Imam, he is required to lighten the prayer for the congregants, due to the Prophet (peace and blessings be upon him) saying: "If one of you leads the people in prayer, he should shorten it, for among them are the weak, the sick, and the old. And if one of you prays by himself, he may prolong it as much as he wishes."