I would argue that in practice it is difficult to remove the batch effect and end up with a completely batch effect free data set. A batch effect removal tool must before removal somehow estimate the batch effect. This estimate has an estimation error, and when the estimate is removed from the data the estimation error will take its place and may likewise act as a batch effect. This can be hard to detect in a real setting, but in a simulation study this can be directly observed by comparing the adjusted data with the "true" data.
I find that plotting (PCA, clustering) the data after adjustment is useful in order to inspect if the samples cluster mainly by biology as long as this grouping by biology information was not used in the batch effect removal. When batch and biological group (assuming there is one) are severely confounded, the "after" plot may be misleading if the same information is used in both the batch removal and the inspection plot. I observed this problem using simulated data and comparing what the plots indicated (PCA, Hierarchical Clustering, PVCA) with what I could deduce looking at the difference between adjusted data and "true" data.
I found the simulations so useful that I made a shiny app for it which you can test here:
https://vegard.shinyapps.io/batch-adjustment-simulator (read help)