With 20,000 systems in the bubble I doubt any individual system would really cause a problem if destroyed, in that sense.
- various organisations could have their headquarters' attacked but any organisation big enough that we've heard of it will have offsite backups, multiple offices across various systems, and so on. Azimuth is a fairly small player in this respect, was overly centralised around Wycherley, and still managed to survive the death of its leader and much of its senior staff, as well as considerable loss of assets and the destruction or inaccessiblity of many of its facilities, without losing everything. It wouldn't be pleasant for the Federation to lose Sol permanently (let's say Cocijo somehow sends the star nova, rather than just destroying Earth) but it'd be largely survivable.
- the bubble's least-common production economy type is High-Tech and that's still 1000+ geographically-dispersed systems to take out
- Sol has an extremely high population but it's still less than 1% of the bubble population: again, a tragic event but not one threatening to humanity as a whole. Most systems are much smaller and just rounding errors.
- from a CMDR perspective the engineers are a little less replaceable but as Palin demonstrated (quite a few years back, now!) they can always run away and set up somewhere else.
- Powerplay capitals could even be destroyed - the Power would need to designate another Stronghold as the new capital but could again carry on; on the other side the Stronghold Carriers mean that Shinrarta's major selling point really isn't that important any more
It's certainly hard to think of a better target than Sol for getting people together to defend it, though.