I would say the easiest solution would be to change the nature of the scene. Portraiture can be all about spur of the moment shots, but even if you want that kind of aesthetic, I think one can still achieve it without losing sight of the other aspects that make for a great photo.
When making portraits, you should always be aware of what surrounds your subject. In the sample you posted, the background has a few problems:
- Obviously, the scene's dynamic range is huge thanks to a dimly lit interior contrasted against a bright sky out the window.
- The background doesn't bring any intriguing quality to the photo, compliment the subject in any great way, or offer any kind of consistency (its split down the middle, one half darker and one half very bright)
- It leaves an odd shape sticking out of the subjects head (a ceiling fan I believe, but an odd protrusion from the head nevertheless).
I am assuming you are shooting "from the hip", without a tripod, or any explicit ability to use multiple flash to control your lighting, etc. When taking a portrait, try to angle yourself, the subject, and the background relative to each other that it will produce a pleasing result. Try to make the subject's face more evenly lit (in your sample, one side is fairly deeply shaded, the other side is fairly lightly shaded, resulting in a fairly broad range of contrast across his face), or at least, shaded with light that differs by only a few stops, rather than ten stops (unless a high contrast portrait is what your after.) Either put the subject all in artificial light, or all in natural light, but avoid blending the two as that will push dynamic range to or beyond the limits of your camera, resulting in things like blown sky or even blown skin highlights. If shooting outside, or lighting your subject with brighter natural light, try to take your shots when they are illuminated more directly (but not necessarily head on) to improve exposure, and still keep some appropriate shading to bring out their profile.
Try to find a pleasing backdrop. Even if it is going to be blurry, it still matters...its a complimentary factor of the scene. Avoid allowing any background elements to "protrude" from your subject, especially their head. Poles, trees, ceiling fans, anything else that might produce an odd interaction...shift yourself relative to the subject such that they don't interact. Boke can be a huge factor in portraiture in general, especially if there are OOF point highlights that can be nicely arranged around your subject...so keep an eye out for that kind of thing, and use it in your scene.
All of this may sound like a lot, but once you practice it for a while, noticing these "alternative" factors in your portraits will become second nature, and putting them all to good use will become a natural thing, requiring very little thought.
"Am I right to consider the only solutions here are taking two photos and merging them?"Nope! You, as the photographer, have complete control over your scene. You don't have to wait for anything...just make it happen! :) Move yourself, move the subject, move the background, move em all if that's what it takes. Never forget that its about the subject, but the surroundings matter just as much. I've provided a detailed answer below.