Tldr:

Having too many cultures that have not established a "market share" in politics makes the, people who run a country, job harder as it has to contend with dealing with the potential of new cultures forming and the inevitable culture clashes that follow as differing values and ideals will demand different things.

It fractures and dilutes points of control which encourages politics to try ensure loyalty though aligning itself with views of the majority.

End tldr

Unironically, Stellaris is probably a decent example of the thought experiment played out. Unless a species is built with ideals of the intergration and/or has its proper foundation set then it can quickly spiral out of hand as you have to deal with " a hunded voices asking for one thing".

It is far easier to control and secure a foundational majority based off of one species as it can be more easily guided towards an established outcome.

Adding too many "outsiders" has the potential to cause an imbalance and a shift in thinking which then requires a new paradigm to "herd the sheep" as it were, while still trying to maintain a standard that the base species has become accustomed to.

If it not carefully controlled, it can potentially lead to a fracturing of opinion and thoughts which is a lot harder to manage and "guide" as one runs the risk of isolating one group and in doing so opening up the potential cascade of problems if the ignored minorities builds up steam which then forces leaders to contend with trying to figure out a way to maintain control over the many species bases while still doing it in a way that causes the least amount of disruption to their control.