Why doesn't the night sky keep on getting brighter and brighter every day?
This assumes that the stars formed at the same time as the Earth.  This is not the case.  Stars had been forming for billions of years since the Earth formed.
The Earth didn't form in a single day, but for convenience let's pick one Early day in the Earth's formation as &quot;day 0&quot;.
On day 0 light from many stars that had been travelling for years reaches Earth. The night sky is full of stars.
On day 1 light from those same stars that was emitted one day later reaches Earth, the sky brightness doesn't change.
On day 2 the same and so on.
Over time some stars will have moved nearer, some will have moved away, some stars will have reached the end of their life and some will have been born. But, on average there is no change.