That's a common misconception about Mode 7. And, well, it doesn't really work how I expect you think it does. This will be a little technical but I'll try my best at explaining.
The SNES has 8 background modes (abbreviated to BG mode or just mode from here on), numbered 0 through 7. So you can't "turn off" mode 7, you pick a different BG mode.
Mode 7 is the only BG mode that provides a background that can be rotated and scaled.
The top-down Flammie view makes use of the scaling to ascend (scale down / zoom out) or descend (scale up / zoom in) and rotates the background to represent turning so that Flammie can always face top-of-screen or bottom-of-screen.
The fake 3D projection lots of SNES games do makes use of rotating and clever use of scaling: it's rotated to face the desired direction, then every scanline the scale is changed to "zoom in" so that the top of the fake 3D projection is not stretched and looks far away, and the bottom is highly stretched (zoomed in) and looks close.
If you used a different BG mode for Flammie flight, north would always be up on the screen, and you couldn't zoom in or out. Turning would turn Flammie rather than the background (if the controls were unchanged). You'd also need art to represent Flammie facing different directions since there's no sprite rotation with baseline SNES. Some of the SoM bosses that do shrink / grow (e.g. the slimes) or rotate do so because those fights use mode 7 and put the boss's art on the mode 7 background layer so they can be scaled and rotated.
There's an additional wrinkle in that graphical data for the mode 7 background is a different format than the other 7 modes, so you can't just flip between them and use the same graphics: sprites and mode 0-6 backgrounds require one format, mode 7 background requires another. So there's no easy way to even try it out, all the world map tile art would need to be processed into the format needed for mode 0-6.
The globe map (also mode 7) and flat map (mode 3), don't even use the world map tile art, they have a palette that represents each tile as a single color, and use that palette to construct their respective tiles at run time.
Normal gameplay uses BG mode 1. The menu screens use BG mode... uh, 5 maybe? I'm not 100% sure on that.
You can approximate non-mode 7 flight by facing exactly north (you're facing exactly north when you first summon Flammie), and being at a height where tile pixels match screen pixels in size (not sure what height that'd be).