A CSV file has a constant number of columns in each row, like a rectangular spreadsheet.
If you have LINESTRINGs, then each feature could have a different number of X-Y coordinate points making the line. How are you going to put them in a rectangular spreadsheet?
Yes, you could make the spreadsheet non-rectangular and pad each row with enough columns for the longest LINESTRING, but... ick.
The WKT format gets round this by storing the variable number of X-Y coordinates in a single text string.
Without knowing why you think you need LINESTRINGs as X-Y in a CSV, I'm not sure we can help more beyond "Can't be done".