Obviously you can't get it exactly the same unless it were a system where everyone learned via video tutorials prepared in advance. Anyone who's been through any amount of schooling had some teachers that were really great and some that were plain shit.
100% perfect isn't going to exist and realistically if you get to 95% it's likely good enough because the remaining 5% is so expensive that it's no longer feasible to try as there's something else that the money could be better spent on.
The Finnish school system is regularly lauded as one of the best and it's done away with much of the pointless crap that the U.S. system indulges, such as constant standardized testing. Obviously it's not as simple as adopting their system exactly as it is without accounting for cultural, geographical, or other differences that might cause issues or skew the results in their favor, but what we're doing now isn't working.
Also, I realize that not everyone is equal and that you can't realistically give everyone an equal start. As you point out, some parents will devote more resources to their children's success than others. The government can't practically enforce mommy and daddy reading a set amount of time to their children every night nor can it control for individuals who have been more successful passing that on to their children, either genetically or in terms of physical assets.
My argument is that it's better to spend the extra money on improving education and the situations of the least fortunate that it is to jail them or deal with the consequences of having an underclass. A few people can still rise from that, and to some degree that'a s great part of the U.S., but most will just be a net drain on society when there's an opportunity for them to be valuable contributors. Just because it's impossible to get everyone to be a net positive, doesn't mean that there isn't a point along the cost-benefit scale where investing more into education and the poor doesn't yield a better outcome for the country as a whole.