Take Uber as an example: yes they've raised prices to become profitable, but not to the insanely profitable levels they could if they had a true monopoly. People will stay on Uber when the competition is still at a roughly equivalent price, but will switch if Uber raises its prices enough.
Uber Eats is different, since its a 3 sided market where the cost is paid by the restaurant rather than the user.
AI appears it's going to be more like Uber the car service. Claude can charge $200/month, but charging $2000/month seems unlikely to work. I'm sure many would be willing to pay $2000/month if they had no alternative, but there are alternatives.
I like to call this the "Yahoo Effect"
Some of that is seeking to kill competitors before they can get established. That's normal and has been around for generations, if not since trading was invented.
But most of what we've seen during the "enshitification age" has been to burn money until you achieve a critical mass of users. However, this only really applies to social platforms where the point of it is communicating with people you know. That's the lock-in. You convinced Grandma to join Bookface and now you feel bad leaving if she doesn't leave at the same time, and more importantly, who wants to join Google Square if nobody else uses it?
That's not going to work for AI platforms.
What I do see potentially working is one method that email platforms use to lock in users: having tons of data you can't export/migrate. If you spent lots of time training your AI by feeding it your data, that's going to make it harder to leave.
So far none of them have capitalized on this (probably due to various technical reasons) but I expect it to start eventually.
Coincidentally, bringing your own address that can be migrates away is somewhere between impossible and expensive.
https://www.zoho.com/mail/zohomail-pricing.html
A few DNS hosting companies still bundle in a few free email mailboxes with registration costs but that is becoming more rare.