Praise be to Allah, Lord of the Worlds.
In principle, an Imam should take the conditions of those praying behind him into consideration since some of them could be weak or sick. He should also deliver the prayer in its perfect form, as did the Prophet (PBUH).
Anas reported: "I never prayed behind an Imam who was briefer and more perfect in prayer than the Messenger of Allah (PBUH)." {Related by Muslim}.
When it becomes hard for the praying people to complete reciting al-Faatihah, make Tasbeeh or attain submission because the Imam rushes in his prayer, then the latter has transgressed and failed to shoulder the responsibility entrusted to him by the Prophet (PBUH) who said: "The imam is responsible......." {Related by Abu Dawoud}.
In case the Imam rushes in his prayer, it is incumbent on those praying behind him to deliver the minimum availing form of the pillars and achieve a level of submission where the organs are at rest before moving to the following pillar, even if that means lagging a bit behind the Imam. No matter what the case may be, you should advise that Imam to slow down and deliver the prayer in its perfect form. Allah's Messenger said: "The Salat is not acceptable if a man is not at rest - meaning his back - while bowing and prostrating." {Musnad Ahmad}. And Allah Knows Best.