Why can't I modify someone else's transactions, if I have their signature data?

[Bitcoin]

Why can't I modify someone else's transactions, if I have their signature data?

As I know, signature system is adding signature to end of transaction. And doesn't hash transaction, so others can know my signature.

If I can send a message directly to the node, can I use other's signature and send currency to me?

For example, Alice make a transaction sending 1bitcoin to Bob. Then Alice will send her digital signature to nodes. And nodes will verify it is from Alice and share the transaction with address, signature, etc.

At here, I can know her signature and can send a transaction with her signature. Then nodes will verify this transaction is from Alice and share it.

I'm very beginner of cryptocurrency, so can you let me know where has problem?

Source: Why can't I modify someone else's transactions, if I have their signature data?