I was looking through my collection for earlier examples of these flimsy jackets and I found this one:
Terminator 2: Judgment Day (1991) [PILF-2555]It's was released 1998-03-27 which is quite interesting so a good deal earlier than some of the other titles.
So I thought I'd check the prices on some of these titles to see if ones in flimsy jackets were priced cheaper.
Japanese flimsy jacket prices: Terminator 2: Judgment Day (1991) 6700 yen
Mummy, The (1999) 6700 yen
Psycho: Deluxe Edition (1998) 5700 yen
General's Daughter, The (1999) 5700 yen
For Love of the Game (1999) 5700 yen
Snow Falling on Cedars (1999) 5700 yen
American Beauty (1999) 5700 yen
Mission: Impossible 2 (2000) 5700 yen
Sixth Day, The (2000) 5700 yen
Japanese thick jacket prices:Independence Day: ID4 (1996) 6800 yen
Die Hard (1988) 6800 yen
Die Hard 2: Die Harder (1990) 6800 yen
Die Hard 3: With A Vengeance (1995) 6800 yen
Kundun (1997) 5700 yen
Parent Trap (1998) 5700 yen
Star Wars: The Phantom Menace (1999) 7800 yen
Blair Witch Project, The (1999) 4700 yen
Fight Club (1999) [PILF-2835] 5700 yen
Other Sister, The (1999) 5700 yen
World is not Enough, The (1999) 5700 yen
Anna and the King (1999) 5700 yen
Bringing Out the Dead (1999) 5700 yen
Beach, The (2000) 5700 yen
X-Files: 7th Season vol.4 (2000) 6700 yen
It seems pricing for a flimsy jacket was dropped from 6700 to 5700 yen over time.
Thick jacket prices also dropped from a typical price of 6800 to 5700 yen in general so both were eventually priced the same.
It looks like Pioneer originally did charge a little more for thick 2LD sleeves but later reduced the price to mostly 5700 yen across the board no matter what style of jacket was used. So they were probably considering introducing the new style flimsy jacket to reduce overall costs as substance has suggested.
There appear to be a few sneaky exceptions where they decided to bump the price back up for say Star Wars: The Phantom Menace to 7800 yen when all other 2LD titles before and after were 5700 yen or cheaper! They obviously knew that Star Wars: The Phantom Menace was going to sell a lot so they milked it! The funny part is that because it sold in such high quantities it is the least valuable one in that series today even though it was originally the most expensive.
Another odd one is X-Files: 7th Season vol.4. Unlike vol. 1, 2 and 3 which came in expensive boxes vol 4 was just a standard thick grade 2LD sleeve with 2 discs same as the others I've listed yet it was 1000 yen more expensive being priced at 6700 and not 5700 yen. I'm guessing they also thought that more people might buy that one to complete the set so they bumped up the price again as there appears to be no other justification given the standard packaging.
Interesting also that Blair Witch Project was the only PILF-28 2LD title that was priced at the much lower cost of 4700 yen even with the thick style jacket being used. This was almost certainly because the budget for this movie was significantly less than every other movie in tha series and it also featured new actors who were completely unknown at that point so likely very cheap to hire!