I'd break it down like this:
ENTJ - some people would like their leadership, their focus, their competence, and possibly even their money
INTJ - some people would like their intelligence, their wit, and they're good at many things.
ENTP - they can be funny and good sources of information to analyze, but it's INTP's who really like analyzing info all day.
INTP - they can be really unusual and funny, and they are very low maintenance and are often okay staring at the ceiling or the wall for hours depending on which comfortable position they happen to be in, although, they'd rather be reading a book, playing a video game, watching a video, or surfing the web. A lack of hygiene and/or grooming and a lack of social interactions, or at least comfortable, high quality social interactions, can help ensure that your INTP will be yours exclusively.
All of that stuff sounds so cold and unappealing to me, and I can't understand why somebody would want to be in a relationship for any of that without it being based in fear or compromise.