So I know that in early British tanks that were equipped with 2 pounder (40mm) guns not having a high explosive round for anti infantry use was considered a huge setback for early British forces. One of the reasons the British liked the Grant tank so much was the high explosive 75mm gun it had. I am curious to why though the original 40mm guns were not provided with it. There were 40mm anti aircraft guns that had HE shells so what prevented the British from designing a similar shell for their tanks.
There was, indeed, a 2pr HE round. It was not, however, issued to tanks.
The first problem is the thing is basically useless, it has a ridiculously small HE filler, and required as near to a direct hit as makes any difference. The second, as I am led to believe, was some bizarre inertia which said that lobbing HE out of cannons was an artillery job, so the AT guns were issued the round. I have not independently confirmed this, however.
As filler content is basically a square function of radius increase, the 57mm 6pr had a tolerable “boom”, and the 75mm was quite acceptable.