What if BTC will be implemented as a legal currency in all countries?
What will be the impact to its integrity and the management of BTC?
This is possible but unlikely to happen because there are countries that don't trust bitcoin instead they just want to create their own coin that they can regulate. But if all countries accept bitcoin as a legal tender there will be a positive and negative effects. The positive effect is since all countries accept bitcoin as a legal currency people who don't trust it will start to trust and use it, the price will rapidly rise until it reach it's limit because bitcoin supply is limited. The negative effect, Due to a lot of users there will be a transaction congestion in the blockchain and transaction fees will be so expensive and also like others said bitcoin will be taxed and the time will come that people will lose interest of using it.