I'm a bit confused - you seem to be starting from the assumption that all schools prescribe 6 GCSEs for their students and all students take 10 GCSEs. This simply isn't true.
There are already schools where everyone does 8 GCSEs, schools where everyone does 9, schools where everyone does 10, schools where everyone does 11, schools where different people do different numbers (normally by, for instance, higher sets doing Eng Lang and Eng Lit and lower sets only doing Eng Lit, higher sets doing triple science, lower sets doing double or single)... it's simply not a big deal (provided you get to do 8 - fewer than that and you start closing doors for yourself).
There's also a mathematical reason why your suggestion doesn't work. Some people are always going to get low grades in their GCSEs because they just don't have the level of ability needed to achieve passing grades. If a school only allows its high achievers to take a small number of GCSEs, they "lose" the statistical advantage that they'd get if those people get lots of top grades to counterbalance the low achievers' low grades. It's not as bad as it used to be because the rules have been tightened over the years - time was that schools would be entering their top students for 12, 13, 14, 15 GCSEs, they'd be taking maths and English every session from year 8 or 9 and so on, because all those passes "counted" in their stats and it was better for them if someone got 15 grade Bs than 9 grade As, and they quietly ignored that these kids were going to have to list vast numbers of maths resits in their UCAS form. Multiple attempts don't count for the school's stats now, nor do enormous numbers of subjects, and oh look suddenly nobody takes enormous numbers of GCSEs, or does early entries, any more. If schools thought that reducing the number of GCSEs people took would make their stats look better, they would do it.