I don’t use tmi.js due to it not being kept up to date for a long time, but getting an App Access Token isn’t particularly complicated https://dev.twitch.tv/docs/authentication/getting-tokens-oauth/#oauth-client-credentials-flow all you need to do is make a POST request with the required params, and you’ll get back a token!
I think the reasoning behind the webhooks subscriptions endpoint requiring an App Access Token, is that a Client-ID is potentially public, so by requiring a token it means only you will be able to access it and which will help reduce the chance of your callback URL being made public, and more generally stops random people being able to see what webhook topics you’re subscribed to.