I'll be honest, my initial response to this post was not favourable. However, after chatting with the lovely @ryivhnn, I realise I have a bias. You see, my daughters were failed by the school system in different ways (in England and Australia), which is why I decided to change to educating them at home. So I'll take this as an opportunity to just put some thoughts forward from the perspective of a mother who has experienced both the school system (not all bad, incidentally) and homeschooling.

dedicating themselves at home only to play.

I realise something could be lost in translation here, but for many homeschoolers learning through play is key, so this phrase feels like it's separating education from play and writing play off as useless. When you take something from the realm of fun then children and even adults aren't going to be able to find any passion or interest in it.

many parents have told the preschool teachers that they cannot carry out school activities with their children for many reasons: they do not pay attention, they say they are bored...

While some parents could just be making excuses, because they are struggling, my initial response here is that if the children don't pay attention or find it boring, then what is being done wrong in the material provided? The right kind of material, if put out on a table in reach of children, should grab their attention enough that they want to interact with it or ask what they can do with it. Of course, every child is going to be different in what grabs their attention, so different options could be useful as well. I realise that what you as a teacher provide the children may be dictated by the school system, so I don't know if you have any influence here, but it could be an option if you do.

The forced approach to learning at an early age can put someone off learning for life and that's the last thing anyone wants. My youngest daughter was put off reading by the school's approach and it took me months to undo that. I'm an avid reader myself, so I was heartbroken to think she might miss out on all that literature. Thankfully she now, no longer has an aversion to reading and has spent many hours absorbed in novels.