once you caught everything you'll only carry 3 to 5 different lures with you anyway, because most of the fish arent worth to catch them
ninja betta, titanic saw, emperor and the two which are required for popping the S ranks: thats all I aim for from time to time

I usually have around 25-30 things in my inventory and even during fishing progression when I carried 20-30 different baits with me I never had issues with free inventory space (40-50 slots left all the time)