but if you select a group, the traces don’t follow the group when you move it
Yes, thats a weakness in the Kicad pcb editor and makes modifying existing boards harder than necessary.
But fortunately the next evolution step (upcoming Kicad v8) is already under way and allows the drag operation with multiple footprints (== a selection of footprints), which is a step forward. (This extended feature is not mentioned in the new-features-thread Post-v7 new features and development news - #5 by mikebwilliams , albeit I consider this a important improvement).
The dragging of a selection including tracks+vias is still not supported.
If you want you can already test this feature with the current nightly development version v7.99. The nightly version can be installed in parallel to v7. Be aware that saved projects later can’t be opened with v7.