Bash – How to parse input file once and send to two separate streams and display side-by-side

I've got the following script:

#!/usr/bin/env bash
# Script to generate MD5 hash for each line.
[ $# -eq 0 ] && { echo "Usage: $0 file"; exit 1; }
file=$1
shopt -s expand_aliases
alias calc_md5='while read -r line; do md5sum <<<$line; done'
paste <(sort "$file" | uniq | calc_md5) <(sort "$file" | uniq)
times

which prints MD5 checksum for each line, side by side, so exactly how I need it. For example:

$ ./md5_lines.sh file.dat
5c2ce561e1e263695dbd267271b86fb8  - line 1
83e7cfc83e3d1f45a48d6a2d32b84d69  - line 2
0f2d633163ca585e5fc47a510e60f1ff  - line 3
73bb3632fc91e9d1e1f7f0659da7ec5c  - line 4

The problem with above script is that it needs to read and parse the file twice, for each column/stream. Ideally, I'd like to sort and make all lines unique and use it as the input only once.

How can I convert the above script to parse the file only once (sort & uniq), then redirect output to two different streams and display lines side-by-side, so it can work quicker for the larger files?

Here is my another attempt:

tee >(calc_md5) >(cat -) \
      < <(sort "$file" | uniq) \
      >/dev/null
times

but it prints the streams separately (not side-by-side).

Ideally, I'd like to use paste, the same way as tee, however it gives me the error:

$ paste >(cat -) >(cat -) </etc/hosts
paste: /dev/fd/63: Permission denied