The best that The Oxford English Dictionary - the word bible - has to say about 'poverty' being the collective name for pipers is that it is an "alleged" name. In fact, it was just one made up by a 15th century prioress called Dame Juliana Barnes. She created a collection of such words in The Boke of St Albans, published in 1486.
This was devoted mainly to hunting and creature terms such as an exultation of larks, a parliament of rooks and a murmuration of starlings.
Since these early days, many others have been created such as a pride of lions and a skulk of foxes, which describe the character of the creatures. Others are just onomatopoeic, like a gaggle of geese and yet more suggest real or imagined behavioural characteristics such as a business of ferrets and an unkindness of ravens.
Collective nouns have been described as "one of the few aspects of etymology that invite the user to coin his or her own at will". Today, these collective names are often composed to make fun of a given group of people such as a flutter of ladies-in-waiting, a flourish of strumpets - for a group of prostitutes! - a deceit of lawyers or a yawn of politicians.
Since this area is so open to creativity, we often find that there is more than one term used...foxes have dens or earths, wasps have nests or bikes and so on. It's really not worth getting worked up about, since the whole matter is so fluid.
So...why not just make up your own, Cybele? Lots of other people have, including Dame Juliana with her 'poverty of pipers'! Certainly Jeffro's suggestion of a 'drone' is vastly more relevant than a 'poverty'. Pipers nowadays - 700 years later - are no more likely to be poor than any other band of musicians!