pushd within a pipeline says it's adding to the stack, but it's not?

I'm working on a modification of [this approach](https://superuser.com/a/608622) to automatically saving and restoring bash's directory stack state when using pushd and popd. For some reason, my code to restore the saved state isn't working -- I'm calling pushd on the right entries, and it says it's pushing those onto the stack, but afterwards, dirs -v is unchanged! I have some directories, one per line, in a file, and I'm using this to recreate the stack:

tac $BASH_DIR_STACK_FILE | sort | uniq | while read -r dir
do
    echo $dir
    pushd -n "$dir" > /dev/null
done

When I run that, it works as expected, and claims to be pushing each of the directories. But afterwards, when I do dirs -v, there's no change to the stack! Using pushd manually for the same directories works as expected. I also tried the declare approach with $DIRSTACK from [this post](https://unix.stackexchange.com/a/366852/632891) but that doesn't work either. Why isn't my directory stack getting updated via pushd inside that loop?