Process the table line by line. Keep an array of text buffers (@t), if the line contains data, split it on |'s and add each part to a corresponding text buffer. If the line contains only ---'s, output the buffers and clear them.

perl -lne 'sub out {
               s/\s+/ /g, print for @t;       # Normalize whitespace, 
+print buffers.
               @t = ();                       # Clear the buffers.
           }
           if (/^-+$/) {                      # Separator.
               out();
           } else {
               @p = split /\|/;               # Split the line on vert
+ical bars.
               $t[$_] .= $p[$_] for 0 .. $#p; # Add each part to its b
+uffer.
           }' < input
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If the last line in the input is not a --- line, you'll need to add

}{ out();
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to the end of the script to print the last accumulated buffers.