I wonder if the writefds argument for the select function is for
non-blocking write purpose because I don't really see the real use of
this argument for blocking write. It would be only useful if in the
select loop when an fd is ready for writing then some data can be
write to it without "for" looping on the write.

Am I correct ?

In my own amateur way, I could attempt to answer your question.  If the
fd is non blocking, you could just have a for loop, where you keep
attempting to write.  The problem with this is that going around this
for loop will use up a lot of CPU cycles.  On a multiuser system like
Unix, these CPU cycles could have been used by some other process.  Or
if there is no other process that needs to work, the computer could
execute a halt instruction, thus saving the CPU from heating up.  But if
you wait upon a select command (even if it has a timeout), you give back
that time to the kernel, and the kernel can give that time to a process
that has real work to do.

sockets are off-topic in comp.lang.c
you should probably try a UNIX news grooup.