To move your capital away from your species' homeworld may be a good idea as a gameplay strategy, but it doesn't make any sense from a roleplay perspective.
If humans had a galactic empire, do you really think they would decide to make Whateverplanet their new capital, and relegate Earth to a small perpheral planet of no importance ?
This has happened in a lot of sci fi settings. Potential Stellaris examples:
Xenophiles (particularly as other species gain more prominence in government) may look to establish a new capitol that has less ethnocentric baggage associated with the founder specie and celebrates the empire's diversity.
Xenophobes may wish to relocate the heart of their empire further behind their borders, away from the influence and reach of capricious aliens.
Similarly, militarists may relocate to better reflect the strategic necessity of the war effort - whether that's closer to provide more direct leadership, or further away from the front to secure the high command.
Spiritualists may want to remove the crude organs of government from their ancestral cradle so it can be properly curated as a holy shrine world.
Materialists are a callous lot and their ethos description even says traditions and superstitions should be abandoned. I imagine many would shift the capitol to the most efficient option without much regard for the symbolism.
Plenty of sensible RP justifications with a bit of imagination.