My personal 2 cents...
Hand Mortars are somewhat overrepresented. Considering the royal foundry of the prussian army,
only made about 300 of them in a 70 year period, and the prussian army easily expanded to several
100.000 Soldiers, they were not that common, even at their "peak".
They were a product of the artillery and siege warfare advances of the time around 1700.
But the shift towards more open battle, the sucess of the coehorn mortar, meant their was no
real use for them anymore. So around mid of the century all efforts to make them a more
common military weapon were halted. And the obscure gadget gradually become even rarer.
But there was no real withdraw of the weapon either.
Some later made examples often have "naval" in their description. Looking at the Nock
volley gun, they put some effort into increasing the lethality of boarding parties in the
late 18th century. Wouldn't be a far fetch that they revisited the concept of the hand mortar
for the same purpose. On a moving and cramped ship, the higher flexibility of the hand mortar
is a larger benefit then in a siege.