Paul's explanation is correct. My reply in the following was written before Anurag Peshne kindly re-explained to me what he meant, see comments below. I am leaving my reply as it stands even though it is not relevant because it seems to me cowardly to hide my errors.
A expressão que não funciona como o OP original gostaria de conter:
echo '$HOME/Downloads'
isto é, uma variável shell entre aspas simples, '' . Esta é a linguagem padrão do bash shell para não avaliar a expressão dentro das aspas simples . De fato,
$ echo '$HOME/Downloads'
$HOME/Downloads
$ echo "$HOME/Downloads"
/home/myname/Downloads
Observe a diferença entre usar aspas simples, '' e aspas duplas, "" , que significam: substituir variáveis.
Na verdade, o manual do Bash tem isso a dizer sobre essa diferença:
3.1.2.2 Single Quotes
Enclosing characters in single quotes (‘'’) preserves the literal value of each character within the quotes. A single quote may not occur between single quotes, even when preceded by a backslash.
3.1.2.3 Double Quotes
Enclosing characters in double quotes (‘"’) preserves the literal value of all characters within the quotes, with the exception of ‘$’, ‘'’, ‘\’, and, when history expansion is enabled, ‘!’. The characters ‘$’ and ‘'’ retain their special meaning within double quotes (see Shell Expansions). The backslash retains its special meaning only when followed by one of the following characters: ‘$’, ‘'’, ‘"’, ‘\’, or newline. Within double quotes, backslashes that are followed by one of these characters are removed. Backslashes preceding characters without a special meaning are left unmodified. A double quote may be quoted within double quotes by preceding it with a backslash. If enabled, history expansion will be performed unless an ‘!’ appearing in double quotes is escaped using a backslash. The backslash preceding the ‘!’ is not removed.
The special parameters ‘*’ and ‘@’ have special meaning when in double quotes (see Shell Parameter Expansion).
Em suma, os comandos exibidos pelo OP funcionam exatamente como o manual do Bash afirma, e todo esse negócio está totalmente ligado ao comportamento de xargs .