Steppemum & exotic fruit are exactly right- it isn't a headstart and it can be potentially damaging for many children.
For some, that are from good and stable homes- it won't do them harm as such, it is just such a false economy. If those children attended an actually good nursery they would be amazing, instead of just able to read & write well.
You are also wasting time that should be spent on the really important stuff. All of the academic skills can be learnt through play. There is just so much more to life than reading and writing. Plus those are finite skills. Once you learn to read and write- it won't matter whether you learnt it at 2 or 8. You will never forget it. Now making friends, being a critical thinker, or having entrepreneurial skill - that is deeper level learning that is NOT promoted in formal settings (the list of what is learnt in a play based environment vs a formal one is huge, but these are good examples)
Another issue with things like forced carpet times is that they are forced.
Forcing a child to conform and do things against their will is not doing them any favours. Why not figure out what the reluctance is about- is it a confidence issue? Ok work on that (Children need confidence to thrive in ALL aspects of life, not just school)
Is it a lack of interest? Again work on that. That's the teacher's job: figuring out how to make the curriculum relevant & interesting. Not forcing children to sit still and listen to you because you know everything. I don't know everything. Even if I did it wouldn't do the children much good. I don't want to teach them what to think, I want to teach them how to think. That is the main point of difference.
Also just because a nursery is play based doesn't mean there are no rules, or they don't teach discipline and respect.