Why do Airbus and Boeing have different approaches to bleed air systems?
Nobody can tell you for sure without insider knowledge, and insider knowledge would be confidential in this case, but ultimately it boils down to risk management. Every new development carries a risk of budget and deadline overruns and of problems surfacing in operation and the manufacturer needs to be reasonably certain they can put the product to market before they run out of money.

When Boeing started developing 787, the 777 was selling well, so they had the budget reserve to risk more innovation. And it did have some problems in operation with battery fires. Airbus was in worse position when developing A350, so they stuck to more tried technologies to keep the risk lower.