Several. I just literally do not see the problem. I'm not saying it's absolutely the most efficient way to do a given project, just that it never was presented as any kind of problem to provide both a SSR app with an API. Obviously you just can't reuse already existing API routes and methods that you would if you had structure it as a SPA but you're likely rendering using SSR from structured data anyway which you can just send as JSON or whatever on a separate route.

I've done this multiple times and it's fine. It's really not an issue for delivering projects. I'm not saying I'd do this every time - if the API was identical for both my app/website and any other clients I'd very possibly abandon the SSR approach for the ease of a frontend API that everyone can use identically, but that's a specific project requirement not a general statement on SSR and API development.