You may only redirect the standard input stream from one place. You can't expect to be able to redirect it from several files or process substitutions in a single command.
The command
cat < <(date) <(hostname) <(uptime) <(cat /etc/resolv.conf)
is the same as
cat <(hostname) <(uptime) <(cat /etc/resolv.conf) < <(date)
i.e., you are giving cat three input files, and then you redirect the output of date into its standard input.
The cat utility will not use its standard input stream if it's given files to work with, but you can get it to do so by using the special - filename:
cat - <(hostname) <(uptime) <(cat /etc/resolv.conf) < <(date)
Note also that the last process substitution is useless and the command is better written written as
cat - <(hostname) <(uptime) /etc/resolv.conf < <(date)
or, without that redirection of the output of date, as
cat <(date) <(hostname) <(uptime) /etc/resolv.conf
or, with a single command substitution,
cat <( date; hostname; uptime; cat /etc/resolv.conf )
or, without process substitutions,
date; hostname; uptime; cat /etc/resolv.conf
Related: