There were some early benefits to grid stability, but not to the extent we've done it, no.

At this point, there are a lot of residential neighborhoods that need more distribution and even transmission capacity (because their peak power movement is now exporting power at mid-day rather than the previous smaller peak loads used). And operating the grid has become a much more complicated task.

Does a battery system solve this mid day export problem?

Yes, it prevents the house with the battery from being a tax on the grid. However, the capacity factor of both the solar and the battery is less than if they were deployed centrally.

Again: residential solar isn't worthless, but in many places we've reached the point of diminishing returns where any additional capacity is much less useful-- unless there's an ancillary benefit that justifies it (like backup power for your house when deploying storage).