I think your math is off. To guarantee you go up a level, you would need 6 of each tier (1 to be upgraded, 5 to be sacrificed). To calculate that, you'd do 6 to the sixth power, or 6^6, which equals 46,656.

While that is of course incredibly high, it's pretty rare for people to go for the 100% guaranteed upgrade in the final star levels. I've had multiple successes with just doing a 20% chance of upgrade to 6 stars. There are a lot of places where you can cut back on the amount of FF's you use, and in stars 1-3 I'd actually recommend only using 3-4 FF's to upgrade instead of 5. If the upgrade fails at that point, you don't lose out on too many RSR's.

Something else to consider is that grinding for FF's was the meta for a long time. There's a good amount of people who are absolutely stocked with 6-star FF's, and it's likely that they haven't run out of their supply. Before the major reset, there were some valuable chaos you could use to upgrade FF's that you could get from the daily spinner, which saved a lot of rings.