Why do we like LFSR and PN-sequence in FPGA?
Why does the industry prefer the PN-sequence than other random
  generators?


Because autocorrelation would give only one exact peak. Doing cross correlation of different PN code would give zero result, kind of selective receiving. You send  a sequence to DUT and you receive the response, used in radar, sonar, model identification,...etc


  It isn't a trivial task to generate PN-Sequence word in each
  clock-cycle.


Not needed, as the transmitter sends a signal serially.

EDIT:

Let we have a boat with 4 sonars placed at sides, bow and aft. If each of them sends different PRBS, then doing cross-correlation of received signal with known code you'll selectively reconstruct the received response

EDIT2:
From your linked document, there is also a nice description of the application for these codes:


  A PRBS (Pseudo Random Binary Sequence) is a binary PN (Pseudo-Noise)
  signal. The sequence of binary 1’s and 0’s exhibits certain randomness
  and autocorrelation properties. Bit-sequences like PRBS are used for
  testing transmission lines and transmission equipment because of their
  randomness properties. Simple bit-sequences are used to test the DC
  compatibility of transmission lines and transmission equipment.