I think the circumstance that they pop up "when public transport sucks" is seen more in the US. Jitneys are considered "paratransit" there — fundamentally a substitute. In many Eastern European countries, a common issue was that marshrutki cannibalized existing public transport options by duplicating routes (more on that in the Wiki article I linked in my parent comment). They compete more as equals, not fill an under-served market niche.
By the way, a marshrutka serves one of the last NATO-Russia routes[0]; a very meaningful route in both public transit and diplomatic, cultural contexts. I will concede to you that this is a case of "public transport sucks" to the highest degree, on a global scale.
These route taxis are very versatile, and the diversity of how they are used and their relationships with public transport is huge.
But if a city really invest into public transportation, there's no need in the small routed hailing vans, because they have lower throughput. E.g. in Bogota a good bus system (they couldn't build a subway because soils) performed better than Busetas (aka Marshrutki). They did dedicated bus lanes for high-speed large buses. Although compared to Bogota, typical US/EU city has way lower ridership I think.