It's hardly more private and not less secure at all.

A remote node can see the exact outputs your tx choses for a ring signature, so you lose the pure untraceability that hosting your own blockchain offers, the untraceability that Monero is famous for. Not private. Further, using a remote node relies on a single node for the blockchain, and single points of failure are a lot easier to compromise or monitor than simply hosting your own blockchain. Not secure. Downloading your own pulls blocks from a variety of nodes and achieves true consensus.

It's also not snappier to send because you have to sync to the latest block, wheras you can send to a remote node almost instantly. And obviously the same applies to spending newly received coins.

It is faster to send a tx once own blockchain has synced. I've done both many times. Remote nodes have lag whenever they have to communicate with your wallet when choosing outputs for your ring signature, and the lag can be particularly bad depending on server location. I think I saw a PR where MoneroMooo helped this situation by reducing the amount of data needing to be transferred, but sending a tx from your own computer is still almost instantaneous by comparison.

Really, having your own node is just purer in the spirit of cryptocurrency. You're not relying on any single entity to make things happen. Doing so not only strengthens the overall network, but also makes Monero truly trustless, which is key when it comes to something as important as your own money.