Many Web3 developers have chosen to build dapps because of Ethereum's inherent decentralization:

Anyone who is on the network has permission to use the service – or in other words, permission isn't required.
No one can block you or deny you access to the service.
Payments are built in via the native token, ether (ETH).
Ethereum is turing-complete, meaning you can pretty much program anything.
Web3 has some limitations right now:

Scalability – transactions are slower on web3 because they're decentralized. Changes to state, like a payment, need to be processed by a miner and propagated throughout the network.
UX – interacting with web3 applications can require extra steps, software, and education. This can be a hurdle to adoption.
Accessibility – the lack of integration in modern web browsers makes web3 less accessible to most users.
Cost – most successful dapps put very small portions of their code on the blockchain as it's expensive.
Core ideas of Web3
Although it's challenging to provide a rigid definition of what Web3 is, a few core principles guide its creation.

Web3 is decentralized: instead of large swathes of the internet controlled and owned by centralized entities, ownership gets distributed amongst its builders and users.
Web3 is permissionless: everyone has equal access to participate in Web3, and no one gets excluded.
Web3 has native payments: it uses cryptocurrency for spending and sending money online instead of relying on the outdated infrastructure of banks and payment processors.
Web3 is trustless: it operates using incentives and economic mechanisms instead of relying on trusted third-parties.
Why is Web3 important?
Although Web3's killer features aren't isolated and don't fit into neat categories, for simplicity we've tried to separate them to make them easier to understand.

Ownership
Web3 gives you ownership of your digital assets in an unprecedented way. For example, say you're playing a web2 game. If you purchase an in-game item, it is tied directly to your account. If the game creators delete your account, you will lose these items. Or, if you stop playing the game, you lose the value you invested into your in-game items.

Web3 allows for direct ownership through non-fungible tokens (NFTs). No one, not even the game's creators, has the power to take away your ownership. And, if you stop playing, you can sell or trade your in-game items on open markets and recoup their value.