Here the argument is "Delete" button is not useful in mobile. Because we already have x button.
I have many use cases where you would need "Delete" button instead of x button.
1) Let us say, I have typed in few sentences in my any app. Let's say I want to delete last 2 sentences, out of total 5 sentences. Instead of going to end of the whole content, I would go to the place from which I want to delete those sentences. i.e. I would prefer to go to the end of 3rd statement and press "Delete" and delete the last 2 statements.
2) Let's say I have a big URL which I have copied and pasted in the browser's URL-bar. Now I want only that part of URL which does not need the content after say some "/", in this case I would go to that slash and press "Delete" button and remove the remaining part of the URL. I won't prefer to use 'x' icon to delete from the last content of big URL, because in that case I would need to check, whether the last "/" which I wanted to keep as is, has reached or not.
e.g. current URL is Why don't mobile keyboards have a delete button?
Now I only need the URL upto Questions. I know this is not big URL, but think of it as big url. What would you prefer, if you want URL upto https://ux.stackexchange.com/questions/
What I would prefer, is I don't want content after questions/, so I would go to questions/ and delete all stuff after that using "Delete" button.
These are only 2 use cases, there are many, if you think of.