"this would narrow your market down too much"
How do you know? Can you quantify that somehow?
"people with specific apartment demands > number of people who want an apartment with a view"
The same could be said for every site. There is always a generalization that targets more people.
One essential advice for startups these days is that the initial target audience can very well be small. It's interesting to see that 'too small of a target audience' is the main counter argument in this discussion.
How big was the estimated target audience for AirBnBs original offering to house people on air mattresses?