Can envsubst not do in-place substitution?

Here is the solution that I use:

originalfile="file.txt"
tmpfile=$(mktemp)
cp --attributes-only --preserve $originalfile $tmpfile
cat $originalfile | envsubst > $tmpfile && mv $tmpfile $originalfile

Be careful with other solutions that do not use a temporary file. Pipes are asynchronous, so the file will occasionally be read after it has already been truncated.