It seems that Bitcoin, the security technology, is ready for that price and probably could even support coins at $20k or more.
What's your definition of 'ready'? It was effectively no more or less secure at $200 something and nothing much has changed in terms of infrastructure since then.
I'm not a technical person, so in some ways I rely upon the technical assertions of other people, and their various descriptions regarding bitcoin's security.
Accordingly, I am mostly referring to the hashing power, and the decentralized power of all of the computers that are securing bitcoin. Also, my understanding is that there have been various unsuccessful attacks at the bitcoin's blockchain over the years, and none have been successful and additional security measures have been taken, too.
So, in essence, I am relying on the technical claims that bitcoin is way too secure for its present value and the logical inferences that bitcoin computing infrastructure could fairly easily support a 30x or more increase in the secured value, and we could still rest assured that our coins would be safe.