Bitcoin developers work on bitcoin core. Why don't they create an official bitcoin wallet as well? It will be exactly like bitcoin core, but without the blockchain. I always had that query.
You do not need to bother yourself about this, there are alternatives, there are decentralized spv versions with open source blockchain. There are also very good wallets like electrum. Electrum source code is an open one which is available on github, it is also a good wallet. Bitcoin and bitcoin wallets are so decentralized than for you to be thinking of such wallets, as they actually existing. Try decentralized spv versions or wallets like electrum.