There are assumptions:
1. Maybe the latest version boots?
2. If ToolBox is used - as it is set up? There are no problems?
3. There can be a slow operation because of incorrectly tuned variables.
What settings of variables, cards, columns...?
Somewhere it can is necessary to specify configurations or versions?
If to reduce quantity of variables - something will change?
Free text - does not approach? - https://forum.solidworks.com/thread/223093
4. Does not depend on the computer, the user, group, vault...?
The problem turned out to be the model/assy itself. If an assy is slow to rebuild, has many circular references and in general is poorly made, this will affect the processing of the named BOM. Once we cleaned up the assembly and removed the processing issues, the named BOM performed as expected.