Could be done with lisp also so open the files and make a new one use a blank line as the end marker for each pline. You use the "A" option append to a file. The other and again make a list of file names. If all the csv are in one directory then should only have to point to that directory rather than a file. Trying to remember the get all files say csv in directory, maybe a Lee-mac function. Pretty sure a VL function.
The other thing is say for a CIV3D user you would add a description, this way the plines are not joined together but strung together.
1,219387.14,4348711.49,p1
2,219383.53,4348702.56,p1
3,219373.46,4348677.68,p1
..................
384,219394.62,4348737.32,p2 start of new pline
CIV3D would do the labelling, layer control etc. Other products like Stringer.