Yes, you're right the cladding is lower index, and it is a controlled index! It (along with other layers) protects the inner core. Most data transport fiber is single mode, which requires very tight control of the ~8um 'diameter' of the high index core, but allows for lower loss/km and you don't get mixing of the different modes (think of them as different reflective angles for simplicity). If air was used then any scratch or dirt contacting the core would couple light out.

In fact most multi-mode is graded index and it's much easier to get light into (8x larger core) without a specialized coupler. Note that even single mode allows DWDM- many different high-bandwidth wavelengths, but only 40nm spacing on 1560nm IR. The core, cladding, and outer protective layers are extruded and pulled to extremely precise dimensions, dispersions, and densities into multi-km rolls.

The games that are played to equalize loss and delay among the wavelengths over a range of power and temperature is crazy... and that's ignoring the EDFA optically pumped fiber amplifiers, which let under sea cables work. Amazing tech!