In addition to the answers provided, there's also the fact that in an MVC or MVP front-end, you separate the data from the view. Plus it allows the backend to be useful for multiple projects.
You can provide the same data, and have, for example, one application that displays it as a graph, one that uses it in its logic (e.g. a stock market analyser that doesn't show the stock data but uses it to predict future prices), and one that just displays it directly to the user (perhaps prettified in some way) that can be used as an internal debugging tool for the developers.
If you had the server return HTML, only the last one would be practical. If it returned all kinds of different code depending on the client, then you're bleeding design into function, which should be avoided.
As a general rule, presentation should never be mixed with logic. Thats the philosophy of MVC. The server deals in data and logic. It receives raw data, processes raw data, and returns raw data. It should never care what that data will look like to the user. The client's job is to format and process the data in order to make it presentable to the user in whatever way is specified.