Why does the imam not recite the Basmala aloud?

Because it is a long-established practice to say quietly what is taken for granted, and that is a sign of respect, not neglect. The Basmala is still always recited, and saying it aloud is also permitted.

The Basmala, the words “In the name of Allah, the Gracious, the Merciful”, is a fixed part of the beginning of every chapter. It would be wrong to begin a chapter without it. When the imam does not say it aloud in prayer, this does not mean he leaves it out. He says it quietly before he begins the chapter aloud.

This is a practice that has been handed down over many generations. What is obvious and assumed by everyone is often said quietly. There is no disregard for the Basmala in this, rather reverence for it.

This also explains a common question. Al-Fatiha has seven verses including the Basmala, as the second verse above indicates. When the imam audibly begins a unit of prayer with the words of praise, there are still not just six verses. The Basmala was recited, only quietly.

Some Muslims, for example followers of the Shafi’i school of law, recite the Basmala aloud in prayer. That is also permissible, and both ways are correct. Even in early times no one was criticised or stopped from leading the prayer because he said it aloud. Islam’s attitude here is generosity, not dispute.

So whoever does not hear the Basmala can be sure that it was recited. Every well-taught imam begins each chapter with it, whether aloud or quietly.