Based on observing now 6 different Ks now I agree it is just extremely variable what the kids can do, 2 neighboring schools can be a year or more apart in what the average student can do. Even ones with similar rankings can be extremely different.

Examples of K entry skills varying with location in our rural/regional sort of US area:

Rural public close to us: no kids reading on entry to K in the last few years, half know some letters, some don't know any letters, some count to 10, no other math skills.
Closest town public: most know all letters, some reading a few words, 1-5 per class enter fluently reading beginner reader books. Maybe a few add/subtract up to 10, count by 10s, etc.
Big suburban public an hour away: most reading a few words, some reading real books fluently. Many can add numbers under 5, a few come in doing multiplication or working with easy fractions.
"Gifted" (preference HG, then space available to well above average) private: not that different mix of kids from the upper end of suburban public, but curriculum more interesting, faster pace, teaching towards higher end, good differentiation, no rote instruction.
Non-gifted private in nearby town: more similar to town public, all have pre-k skills, 1 child per year enters reading.
Alternative style private: wide spread, class size so small no average entering skills, depends on year, usually several a couple years ahead by 1st due to individual teacher attention.

I do think it matters in a public school with an average class size what the entry skills of the other kids are. If the entry skills are to the level where it's going to be easy for the teacher to meet their end of year goals, then they have time for answering questions, other content besides reading and math, meeting the needs of the kids who are ahead. If however your child enters a school like our close rural public, where the teacher has an incredible challenge to meet their end of year goals every year and all the kids are about the same to start, then that is truly all they focus on.

In a unusually small class size or one with aids or volunteers etc, it may not matter nearly as much what the level of the other kids is.

Observe a class in person.

Polly