Q: Don't you think they may have written on other objects, like palm leaves or cloth?
A: This has been suggested by Parpola and others, that they probably wrote on cloth or on leaves like birch leaves. I do not know about the palm leaves, palm trees were there of course, but if they had written on palm leaves and they had used a bronze stylus, these must have survived. Nor was there any writing on clay except seal impressions. But perhaps on large barks or on prepared cloth these could have written and this would have perished in the humid and warm climate of the Indus Valley.
Q: But is it likely? For a civilization that lasted so long, they would have seen that these writings on cloth or something like that perished, probably rather quickly. Wouldn't they then have tried to write more important things on stone or clay?
A: The same thing has happened later. Why did not the great and victorious Emperor Chandrgupta who stopped the Greek armies from invading India - why did he not like King Darius record his conquests in stone? The answer seems to be one of culture, it was not in the Indian tradition to make inscriptions on stone and the earliest such inscriptions are those of Ashoka. They clearly show Persian influence. This could be one answer.
The other thing was that in the river valley civilization, in modern Sindh proper, there is not much stone, it is available only in the highlands. In Harappa and Mohenjo-daro brick was the dominant material for building, so stone inscriptions would not have been a natural choice. But they could have used clay inscriptions of course, and they knew that clay was being used in the contemporary Akkadian civilization and they did not do that. They could have used metal for example, since they did write on metal and we have a large number of copper tablets from Mohenjo-daro. Well, this is all some of the might-have-beens of our history. Even the recent Dholavira [Gujarat, India] find - I was disappointed that the very large, nearly 10 feet wide, wooden board contained really nothing but a magnified version of a seal. In fact, I have identified all the 10 characters in that famous board as occurring on seals already in the same sequences. So even the opportunity of a large writing surface was missed. How I wish it contained a very long narrative of the conquest of that city by a warrior!