"Save for web and devices..." is all about file size management. It's hard to argue that a 45MP image (2:3 aspect ratio with the long side at 8191) is slightly too small for a web page (yet, at least). And convenience, I suppose, since it offers one-stop shopping for a bunch of things that would otherwise be separate menu options.
You can use Image→Mode... to change to 8-bit colour depth if you're not already there.
Edit→Convert to Profile... will get you to sRGB if that's what you want. You will need to choose the appropriate out-of-gamut conversion mode; either Perceptual or Relative Colorimetric will be appropriate for a photograph, depending on which colours are out, how much of the image they occupy, and by how much. Perceptual affects more of the image, keeping things in better overall balance, but it may cause unwanted colour shifts. Relative Colorimetric mostly affects only the tones that are out of gamut, but it can leave the things that were changed standing out like a sore thumb sometimes. The other two options are never appropriate for a photo; pretend they don't exist.
Use Image→Size... to scale (not needed if you want full-rez), and File→Save As... to create the JPEG. You would need to "save as a copy" if you don't first flatten the image. And, if desired, leave out the colour profile, which will take up a lot of space in a small image, but will be negligible on larger ones. You should only consider that option safe if the image is saved as sRGB.
The only thing you'd be missing is the option to leave out (or selectively include) EXIF info. You can manage that in another program post-save if you want. And you can always make it an action or script if there's too much clicking for your tastes.