Yes, moving your capital is definitely worthwhile, in fact almost essential (on random maps atleast), There is the obvious additional reason of starting making a new capital before the old one is destroyed (should you be in such a situation) so that the morale loss is removed. In general dont get attached to your first planet, as it is almost certainly not in an optimum location for anything; especially if your first homeworld is next to a wormhole (which has happened to me 4 times), which makes defending it exceptionally hard.

and Not specifically on topic but..

As i see it, the problem with making 1 capital per system is that on smaller stars (say 5-8 planets) you would almost always have very high allegiance, which sort of defeats the point of allegiance. Granted it would be much more sensible on bigger stars, but i tend to focus on why things wont work rather than why they would.

Personally for my mini-mod (primarily for "i wonder what that does" purposes), i have increased the allegiance cap that culture gives from 10% to 35% which not only makes culture much more powerful, but means that your outer planets become significantly more important, as when fully cultured they get you 60% resources rather than a measly 35%. Which as i see it removes the need for multiple capitals, and sort of covers regional governers (ie you could take "Culture" as including the extension of central government)