Why doesn't this bash script print stdout on console when run as sudo?

Question

Consider the following script:

#!/bin/bash

# Define a function to redirect both stdout and stderr
redirect_both_to() {
    local log_file=logfile.log
    exec > >(tee -a "$log_file") 2> >(tee -a "$log_file")
}


# Example functions
one() {
    echo "This is from one()"
    echo "Error message from one()"
}

two() {
    echo "This is from two()"
    echo "Error message from two()"
}

# Call the functions
function main(){
    redirect_both_to
    one
    two
}

main "$@"

When this script is executed without sudo, the output is displayed on the console and it is written to the log file (as expected). However, if I run the same script as root (i.e., sudo ./script.sh), the script exits without printing anything to the console. But both stdout and stderr are correctly recorded in the log file. Ultimately, I want the script to be run as sudo.