The braid test is too light for a baitcaster. You could use it but it will be extremely difficult and annoying - the line is so thin that it will bed into the spool of line. Too give you comparison in diameters - 50# braid is equivalent to 12lb flouro.
So your dads 6 lb braid, i can't even calculate how thin that is.
Commonly, on baitcasters - people tend to start at around 30 and above in # braid. If he wants to go that thin - a spinning reel will be far better of an option.
Birds Nests are 99% user error (my math) - there are a ton of videos out there on youtube that will help your father setup his reel properly to deter bird nests. Make sure he understands, whipping the bait is not always the best way and definitely does not get you the most distance. A solid roll cast will go just as far if not father. If he is overhanding, could be another issue as well. If the line tension is too light, the line is coming off to fast off the spool to where it is not coming off the rod quick enough, thus line overrun and bad bird nests.