I think you might be overplaying the extent of the Maurya empire during Chandragupta’s reign. His expansion of the original nanda empire was mainly to northwest. Not to south. His descendants expanded it to central and southern India.

It fell to Ashoka ( the grandson ) to conquer Kalinga, a hold out state right in the soft underbelly of the original Magadha.

It is also understood that post Ashoka, the rulers were not as effective as their ancestors. And eventually the dynasty was overthrown by a minister. Thus explaining to some extent why further expansion into southern India was not carried out.

Incidentally do you know of organized Tamil kingdom(s) contemporaneous to Maurya empire? Cholas became prominent later on ( much later I d say ).

Most likely because they feared the Tamil kings.

Mauryans Broadsword and Animal Hide Shields are extremely inferior to Tamils Sword and Shields made of Wootz Steel.

Chanakya the teacher and the royal advisor of Chandragupta Maurya states in his book Arthashastra that

Apart from hides and skins, [woolen] blankets and horses, the rest are available in the south: conch shells, diamonds, precious stones, pearls, and golds, are plentiful in the south.

From this, we know they had the knowledge that the south was richer than north but they still continue northwest.

Also Mauryans under the emperor Bindusara fought the Tamil kings and lost the battle. This must be the reason behind why Bindusara's life was not documented or erased from history. Most of his history comes from a 12th-century text called Parishishtaparvan written more than 1,500 years after his death.

But Tamil Sangam literature recorded Mauryans incursions into Tamilakam in Akananuru 69, 251, 281 and Purananuru 175 and they were defeated by the Pandya king Nedunjcheliyan I after his victory he got the title "ஆரியப்படை கடந்த நெடுஞ்செழியன்" meaning "A Pandyan King, who defeated the Aryan intrusion". Nedunjcheliyan I is also mentioned as having a big Army.