In the job queue you will have all the caching procesess sent from Pro that are running simultaneosly. Why is it inconvenient? In a script I don't think the older tool was any helpful than this one. In both cases I think you have to check yourself the status and close the process. Maybe the ArcGIS Rest API can be helful with this
@andrei_ste I confirm you could stop / start / manage caching process for a service from ArcMap without using the job queue or a Geoprocessing Tool. As the caching is running on a server and could takes several days to complete, its inconvenient, sometimes impossible, to keep ArcGIS Pro open in case you need to stop the process.
@MaximeDemers if you save the project in Pro and close it, the process should remain in the Job Queue. I've tested with publishing a new service earlier and it worked. As I stated in another comment you can also close a caching process from ArcGIS Manager. I agree with you and everyone else in this thread that it was maybe more intuitive in ArcGIS Desktop. People maybe got familiar with that flow. But I think Job Queue is fine as well, and since Esri introduced it, I don't think they are gonna give up on it. Hope everything I wrote helps. Take care
