Does TLS interception necessarily require a self-signed certificate? Please explain why

Does TLS interception necessarily require a self-signed certificate? Please explain why

A brief schema of a TLS intercepting proxy - the Client connects to the Host via the Proxy in a way which allows the Proxy to perform a (consensual) MITM.

[Client]  ->  [Proxy]  ->  [Host]

It's my understanding reading references online that implementing a TLS intercepting proxy requires you to:

1. create your own CA signing key
2. have the client trust your own CA
3. the proxy can now basically establish two SSL sessions - Client<->Proxy and Proxy<->Host

This is one way to do this and projects like https://github.com/abhinavsingh/proxy.py use this approach as well as the employer of the author of How can my employer be a man-in-the-middle when I connect to Gmail?.

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Question: is this the only way? Does a TLS intercepting proxy necessarily require a self-signed certificate? If so, can you explain why this is the only way?