When the state buys stuff, the paid VAT always goes right back to it. In some/many cases it's easier to eat this inefficiency, but in some cases it's easier to not do the useless transfer - especially when we're talking about tens of millions of euro and products that only the government can buy. I don't see anything weird about selecting few specific industries where the transactions are always with the government and in high amounts to optimize this useless transfer and bureaucratic busy work away. Nobody paid less taxes than they should have, nothing has changed about that.
> Then, of course, If I produce pistol (as a company), and buy metal, and make a pistol, don't I end up paying VAT on the "added value" ? in other way, even if a company sell to other companies, the VAT% (10% or 90%) does or does not affect profitability?
No, profitability is not affected in any way. The consumer always pays, not any company in the chain of raw material to consumer product. VAT is irrelevant to them, it's just some bureaucracy that needs to be taken care of, but nothing else. It could be 110% and they wouldn't care - VAT is separately on top of the invoiced price and you never treat it as your money, you're just holding it for the government for up to 30 days.
> Then of course you sure have some percentage of buyers who cannot claim VAT (is it small, only consumers? what about not perfectly legal business.... )
Any business can claim VAT back if they choose to. Some countries allow small businesses to say "I don't care, don't bother me, I will eat the difference". This results in losses to the small business, it's done because the paperwork is really hard to do - takes a lot of time and money (you need an expensive tax advisor in many everyday cases). The usual limit of this is around 50k USD of yearly revenue. Above that, it's necessary to fill the VAT forms.