My perspective is that it's selection bias - we only look at the empires which were in Delhi and accord them an undue importance. The kingdoms in Delhi we learn about weren't even the largest, or richest, or even the most long lived necessarily. We only learn about them because they were in Delhi.

For instance, the British didn't conquer India from the mughals, they conquered it from the marathas. At that point, Bahadur Shah Zafar was a vassal of the marathas, whose capital was Pune. But the extent of their empire doesn't really sink in for us until we hear they reached Delhi.

We barely hear of the Ahoms based out Jorhat in the brahmaputra valley. They lasted 600 years, beat back the mughals and had their own neighborly issues with the Burmese. Or the cholas who went from 300BC to 1200s (with peak in the medieval era) with a sphere of influence stretching all the way up the coast of India and to Southeast Asia, and their capital was at Thanjavur. Vijayanagar was a pretty large kingdom with its capital at Hampi. And the Mysore kingdom covered a pretty large portion of South India at its height, lasted 700 years before acceding to the Indian union, and for the last 100 years of its reign, was the cultural center of India (and is still the cultural heart of Karnataka).

Delhi wasn't even really the capital of British India as much as Calcutta was. Calcutta and Shimla (summer capital) were the capitals until 1911, and only after that did King George move the capital to Delhi. And the buildings housing the viceroy and government and all the good stuff was only inaugurated in 1931.

So why do we still focus on Delhi? Some speculations:

• It's the current capital, so a part of our brain just considers it important.

• The people who went on to write contemporary history textbooks and shape the narrative in other ways were based out of Delhi, and probably from the families that benefited from the movement of the capital from Calcutta to Delhi.

• Whoever controls the Ganga plain controls India (because of iron and agriculture), and usually those people base themselves out of Delhi. Or, the area is resource rich and anyone of any consequence will eye this land. Going back to the Mahabharata, jarasandha was the king of Pataliputra, and everyone is super scared of him, and he even drove out Krishna from mathura to Dwarka. And prior to Islamic arrival, Patna was always the capital for this reason. Even now, it's the area in India with an incredibly high population density, and no one becomes PM of India if they don't stand for elections from UP (Manmohan Singh is a notable exception, but we know the special circumstances in that case). However, this doesn't always apply, because there are other resource rich areas, like bellary, which is close to hampi, godavari delta, brahmaputra valley, kaveri delta. The powerful combination of resources in the ganga valley is hard to beat, but not impossible.

I think this has to do with MAINLY the geography of India.

India has been fairly safe from foreign Invasions from all sides: peninsula in the south, Himalayas in the north, and the thick jungles of Burma in the east, making it difficult for raiders and invaders to invade into these territories.

The only passage which was available to the foreign Invaders was the North West passes through the mountains of Khyber.

We know that these passages were repeatedly used by the foreign invaders and conquerors to find their way to the Indian Territories.

Be it the King Darius during the 6th Century BC, or the following raids from the Central Asian Tribes. All of them posed a threat to the Indian rulers for a north West invasion.

The north west passage seems to have not been properly looked after in the earlier periods up until after the Maurya Dynasty. Up until Maurya Dynasty the most prosperous centre for capital was in Bihar, as Magadh.

Only after the Yeuchis and Hunas and Scythians from the central asia invaded the Indian subcontinent that the rulers of India realize the importance of this North West Passage.The Central Asian Tribes came in from Central Asia and developed mainy centres in and around the Yamuna. These centres were further worked upon by the Guptas, and later HarshVardhan established a centre at Thanesar (evidently also his capital) near KurukShetra. Delhi was setlled in by the Tomaras (Rajputs).

The idea that why the later Mughal invaders favour Delhi as their capital in opposition to the other major centres such as Bengal , Varanasi, Punjab, Sindh etc. seems to be that it provided a favourable seat of power to keep an eye for the invasion from the NW and also provide a suitable place to keep hold of the North Ganga Plains. The Ganga-Yamuna Doab region was fairly profitable to the peasants and as a consequence the whole region was quite prosperous for the settlers. In most cases the Islamic Invaders were well connected with the people of the West Asia and wanted to keep a close contact with them through trade and commerce and culture, facilitated by Delhi.

Though Firoz Shah Tughlaq did try to shift his capital to the south (city of Daulatabad) when the Tughlaqs became ambitious towards ruling the South , but the idea like many of Tughlaq's proposals was acted upon in haste and failed to take shape, and thus Delhi continued to be the capital of the future rulers.

Although Delhi can be considered as the POLITICAL and ADMINISTRATIVE capital for many empires and dynasties, there were also other ECONOMIC capitals besides Delhi. Varanasi, Bengal, Gujarat, Masulipatnam all had a bustling trade and commerce and were doing sometimes better than Delhi in terms of economy.

So it was mainly because of the threat of the North West invaders that Delhi has continued to be the seat of Political capital in the past.