What is the advantage of HD Wallets? I have read man resources and questions about HD Wallets. As pointed out in this question on SO, it won't be possible to send funds of a derived child address using the master private key.

In my humble opinion exactly this would make sense if I could create a derived child to receive funds for a specific purpose but being able to spend these funds using my master private key without the need to store each child private key.

Do I miss something here? Why should I use HD wallets if I still need to store each single local private key as well?
The answer you linked isn't wrong; you just stopped reading too soon.

Transactions aren't signed by the master private key itself; they are signed by the child private keys.  But those child private keys were generated from the master private key.  So it's true that all you really need to store is the master private key.

If you have the master private key, and you want to sign a transaction, you don't sign it with the master private key directly.  Rather, you first use the master private key to regenerate child private keys until you find the one that matches the address you want to spend from.  Then you use this child private key to sign the transaction.

For day-to-day use, it is convenient to store the child private key after generating it, so that you don't have to go to the trouble of regenerating it each time.  But for backups, all you really need to save is the master private key.