Babur ruled North India somewhere between 1526–1530 period.
You need to note this period was under the rule in South India by none other than “Sri krishna devaraya” who was pinnacle of Vijaynagara Empire. One of the most powerful kings of Indian history.
Empire covered whole of South India except some parts of Karnataka and Telangana. Even Sri Lanka was tributary of the empire.
Even today ,go to parts of Karnataka, Telangana and Andhra Pradesh you will hear how well respected is “Sri Krishna Devaraya”.
Karnataka people often tell you ,under him , “Hampi was so rich ,gold and diamonds were sold in streets of the city “ Such a flourishing empire it was.
Let's take a look at the empire under him first and get back to our question.
He was a great leader and had faced Deccan sultanates with ease often referred to as “ Destroyer of Turks”.
Hampi was one of the largest and was the richest city in the entire world at its peak. When Vijaynagara Empire fell and power was broken subsequently in battle of talikota in 1565 , it took opponents somewhere around 6 to 12 months to loot and burn the city. You will be amazed to see how magnificent even the ruins are today , if you visit Hampi , a UNESCO World Heritage site. This city is a mirror for our culture and prosperity.
He was respectful to foreign visitors, able administrator , ruthless law maker, tolerant to every religion and was an excellent army general himself.
Coming to the query, you may see Babur , a barbarian who had well versed in war tactics ,proved in battle of Panipat against Lodhi.
But Sri Krishna Devaraya had the most effective army in South East Asia. Vijayanagar empire had an army strength of 7,00,000 and Babur had a mere 60,000. Though one can say , Babur had a strategy of defeating larger empires, but if ever he went to war with Sri Krishna Devaraya, it would have resulted in fall of his emerging kingdom.
Any attempt made of invading Vijayanagar empire, Babur’s Army would have been slaughtered and would have resulted in wiping out the Mughals even before it was well established and Delhi would have soon fallen into hands of winning kingdom.
So Babur was clever and played it safe.