Performance of site when loading 3000+ variables
Yes, large variable tables are a problem.

Variables should only be used for small configuration flags and settings and not to store large structures for example.

But given a large amount of modules, dynamic variables like per-content type things you will sooner or later get into trouble.

No, there is no solution to this problem. The variables system will be replaced with the new configuration system from the CMI initiative for Drupal 8 which will hopefully be better at dealing with this.