Thanks for clarifying the issue.
The behavior/feature that you are suggesting is actually now available in edge mode (with sync select disabled) as well.
Right next to the vert/edge/face/island buttons in the UI, you can find a dropdown titled Sticky Selection Mode. Change the option to shared vertex and that will allow you to select shared edges similar to your suggestion. Example screenshot :
For Sync selection enabled, this is actually a conflict between desired behavior and implementation logic.
By definition, UV sync select will ensure that UV selections and 3D viewport selections (in edit mode) are in sync. In some cases (ex: edge seams), this allows allows selecting vertices that are part of the selected shared edge, but individually the vertices are not part of any edge selection.
As per your suggestion, disabling vertices in these cases would actually be in conflict with the implementation logic for sync select mode.
Implementing your suggested feature/behavior might be possible, but I’ll have to check the code first.