There probably are a lot of examples in the North (they are now part of some "secular" Mosque complex), but it's very apparent in some of the Hoysala temples that were partially/fully destroyed (esp. Halebidu), and in Vijayanagara. It's really quite sad. Then again, I suppose this adequately reflects India's state as a civilization... so SNAFU.
I find that interesting because when I was in Turkey it was common to see the ancient depictions of Jesus Christ on church walls with the eyes scratched off. The explanation given by the locals was the same as what you state for the statues in India.
Technically, it's not the same language, culture, etc. The living culture has changed considerably over the centuries both organically and via outside influences, including Islam.
The surprising thing about India is that it has kept around so much of the really ancient stuff while also adding a huge amount of new stuff along the way. Cultural hoarding, if you will.
It's like the cultural change process is sedimentary, with previous layers being preserved below, while the newer layers get added above, giving a kind of continuity, whereas in other parts of the world, it has often tended to be a more volcanic process, with the destruction of what preceded.
Also, Indian culture long ago accepted what to Western thinking seems like a contradiction of polytheistic icon based religious worship and the belief in a more abstract deity, or even atheism.
In the West, this resulted in the complete disposal of the previous pantheons, but in India, it was rationalized through a "many perspectives" lens where all the viewpoints could be accommodated.
That said, in the same households, people can still be very superstitious, because practically, sometimes being that way helps you explain otherwise difficult things that happen in life.
There are great lessons in both, what they got right and what they got wrong.
But even in the case of Buddhism, one outcome of the repression of Buddhism was the coopting of large parts of it, at least the parts that didn't threaten the Hindu social structure. Whether or not it is widely known today, Buddhism had a major reformatory impact on what we call Hinduism today.