So I was trying to do exactly what was asked in Question on TaskLocalValue.
Say I have a matrix M and I need to calculate eigenvectors of matrices M .+ i for i in 1:100 with 8 cores. But matrices M .+ i are large and I cannot preallocate a hundred of those; I create task-local buffers m instead (and on each iteration I would then do m .= M .+ i). This does the job, but I observe the same core-stopping behaviour as in the original MWE. Anyway, I am not too concerned now that I know that the correct way to do this is to use Channels 