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Could the bitcoin network be destroyed by someone generating endless bitcoin add

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Could the bitcoin network be destroyed by someone generating endless bitcoin addresses nonstop?  I mean it sounds like it would do something really bad to it.

I'm pretty sure at some point a website will take payments in bitcoins and will decide to generate a new bitcoin address for each payment and end up endlessly generating new addresses like mad and do something bad to the network.  Then more will start in.
Generating addresses is CPU-intensive, and you don't touch the network when you generate a new address. It could only cause damage if a non-unique address was created, but this is so unlikely that it's not even worth considering.
Yes.

Also, generating a new address for each payment is the best way to do it. Maximum anonymity because of least re-use of addresses. The keyspace is large enough that we don't need to worry about exhausting it.
If you're generating a new Bitcoin Address for each transaction, people may accidentally send to old ones.  They will have that BA in their Transaction history and may think it's good for multiple uses.  Just something to think about.

The possibility of accidentally sending to a random BA is insanely small though.
When you generate a new bitcoin address, it only takes disk space on your own computer (like 500 bytes).  It's like generating a new PGP private key, but less CPU intensive because it's ECC.  The address space is effectively unlimited.  It doesn't hurt anyone, so generate all you want.