Why does a bash here-string add a trailing newline char?

The easy answer is because ksh is written that way (and bash is compatible). But there's a reason for that design choice.

Most commands expect text input. In the unix world, a text file consists of a sequence of lines, each ending in a newline. So in most cases a final newline is required. An especially common case is to grab the output of a command with a command susbtitution, process it in some way, then pass it to another command. The command substitution strips final newlines; <<< puts one back.

tmp=$(foo)
tmp=${tmp//hello/world}
tmp=${tmp#prefix}
bar <<<$tmp

Bash and ksh can't manipulate binary data anyway (it can't cope with null characters), so it's not surprising that their facilities are geared towards text data.

The <<< here-string syntax is mostly only for convenience anyway, like << here-documents. If you need to not add a final newline, use echo -n (in bash) or printf and a pipeline.

One scenario in which it is practical to have newlines appended to here-strings is when using the read command when set -e mode is active. Recall that set -e causes a script to terminate when it (more or less) encounters statements that generate a non-zero status code. Consider that read generates a non-zero status code when it encounters a string without newlines:

#!/bin/bash
set -e

# The following statement succeeds because here-strings append a newline:
IFS='' read -r <<< 'newline appended'
echo 'Made it here'

# The following statement fails because 'read' returns a non-zero status
# code when no newlines are encountered.
printf 'no newline' | IFS='' read -r
echo 'Did not make it here'