It deserves mentioning that it is very difficult for things in space to fall into each other. If two bodies aren't on a direct collision course they will orbit or slingshot, not "circle the drain until they fall in." The effects that do promote "falling in" happen on very, very long timescales with respect to anything, including stellar lifecycles (you mentioned this but didn't emphasize the extent to which one timescale utterly dominates the other).
We are used to circulating fluid inevitably falling into the center of a drain, but this only happens in our daily lives because viscosity allows the water to shed angular momentum (about the drain) to its surroundings. No angular momentum transfer = no falling into the center, and a galaxy doesn't have a gigantic porcelain fixture anchored to the central black hole to which stars can transfer their angular momentum :)
Actually there is a way that objects orbiting other objects can shed angular momentum: emit gravitational waves. We've observed this with binary pulsar systems; it's expected that it would also be taking place with objects orbiting the black hole at the center of our galaxy. This is one of those "long timescale" effects in most cases, but for objects close enough to the black hole at the center of our galaxy its time scale might not actually be longer than the lifetime of some of those objects. (That would only be true pretty close to the hole, though.)
We are used to circulating fluid inevitably falling into the center of a drain, but this only happens in our daily lives because viscosity allows the water to shed angular momentum (about the drain) to its surroundings. No angular momentum transfer = no falling into the center, and a galaxy doesn't have a gigantic porcelain fixture anchored to the central black hole to which stars can transfer their angular momentum :)