QB Issue Resolution:

No, class tags transactions to allow for reporting, it is not a segregating kind of thing

building an assembly item is not a transaction in that respect, you have not sold it, so there is no class assignment for the build.

Resolution for Issue 'Are there any drawbacks to using class to differentiate inventory assemblies?' available: Yes (Solved).
Source: Intuit Community forum.

Are there any drawbacks to using class to differentiate inventory assemblies?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

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