That's theoretically possible, but in practice the biggest gap I've seen is when someone was a 6 in one and 3 in another.

I work at a startup though, where I need everyone on the team to be something of a generalist. If I was working at a larger company that benefited more from specialists, I would use a different scheme, e.g. dropping the lowest score or something.

Do you think that might be self selection bias then? You might be able to benefit from one or two specialists, but if you even make them an offer, it's as a 4 (or whatever), but another company might be willing to make them an offer as a 6 or a 7, because they have a place for specialists. Not that that's necessarily a problem if you do indeed need generalists, just an interesting possibility to think about if you ever find yourself needing specialists.

I use this framework for giving raises/promotions/feedback to existing employees, not for new hires. With actual employees you have a lot more information, so I believe companies should generally hire cautiously but give promotions and raises aggressively (most do the opposite IMO.)

I did actually have a case similar to one you described, where someone was a very advanced specialist in a narrow area, and relatively weak in others. I was willing to make him an offer at a 5, another company hired him at a 7. I think that was the best outcome.

In another, less extreme case, we used to have one "data scientist" role. We found that this required too much breadth, and people with the same role ended up doing very different things. So I've advocated for separate "data analyst" and "data scientist" roles, each with their own set of 4 competencies.

The place where I work has two separate 'tracks', Senior Engineer and Specialist, and both are considered to be on the same level. Employees can chose which level the want to aim for and then be evaluated accordingly.