SMB3 was designed to be played with Mario turning small regardless of powerup. It's too easy otherwise.
Nintendo clearly changed their mind on this at some point in the early 1990s even for Japanese releases, as both the remaster of SMB3 in Super Mario Collection (1993) and Super Mario Advance 4 (2004) have the 3-hit Leaf/Fire/etc. -> Super -> Small damage system.
Here's a rundown of the damage system changes over the years for all four classic Super Mario Bros games:SMB 1:
2-hit system on all versions (Famicom/NES, All-Stars/Collection, and SMB Deluxe)SMB 2
(aka "The Lost Levels"):
2-hit system on all versions (Famicom Disk System, All-Stars/Collection, and SMB Deluxe)SMB 3:
2-hit system on JP Famicom release
3-hit system on US/PAL NES release, and all releases of Super Mario All-Stars/Collection and Super Mario Advance 4SMW:
2-hit system on JP Super Famicom & US/PAL SNES releases
3-hit system on Super Mario Advance 2