No, that's not how it works. If a business sells to another business, then the buyer is the consumer, and VAT has to be paid. And of course they have to sell with a profit.
Many B2B offers and proposals are negotiated or priced without VAT mentioned, but it is absolutely added to the bill.
The only time it "nets out" is if a business has the same expenses for their purchases as for their sales, meaning they're soon bankrupt.
It nets out to everyone but the final consumer. Imagine 30% VAT rate:
Alice digs up some copper and tin and sells it to Bob for 10€ + 3€ VAT = 13€. Alice remits the 3€ to the authorities on Bob's behalf.
Bob casts bronze bars and sells them to Carol for 39€ + 11.70€ = 50.70€. Bob claims a 3€ refund for VAT he paid Alice and remits 11.70€ to the authorities on Carol's behalf.
Carol makes a sculpture from the bronze and sells it to a customer for 1014€ + 304.20€ VAT = 1318.20€. Carol claims a 11.70€ refund for VAT paid and remits 304.20€ to the authorities.
The end customer ends up paying 100% of the total VAT (304.20€). Everyone else nets out to 0.
That's just mental gymnastics. In the end the customer pays 100% of the costs a business has, that's completely obvious. Then we can say that businesses don't pay payroll tax either, because all salary costs are also baked into the price of the final products to customers.
You're correct with your calculations, but it's not honest to say that the customer pays the VAT and therefore it nets out for a business.
What's happening is that a business gets refunded by the government for any VAT they pay. Alice charges Bob VAT. Alice remits the money to the tax authorities who then refunds Bob the money they paid.
If after paying payroll taxes, the government decided to hand all the money back, that would be VAT. The only one who doesn't get refunded is the final customer.
Many B2B offers and proposals are negotiated or priced without VAT mentioned, but it is absolutely added to the bill.
The only time it "nets out" is if a business has the same expenses for their purchases as for their sales, meaning they're soon bankrupt.