Ooh, interesting question....I'm task-based and currently have a FC who will likely need a long term family and so I've been giving this question a lot of thought recently.
I think I'm unlikely to agree to her staying permanently and I have a few reasons - a big one is that I have a young child myself, and I like to have time in between placements where we can have time/holidays to ourselves. I also wonder whether I'd have the energy to start again with a new placement if I had a FC live with us for several years...particularly if it was an easy several years with us all just plodding along doing the family thing.
I also think if I had a FC with us long term and they really became part of the family, wouldn't I then just let them stay on/keep supporting them after 18 (if that's what they wanted too), which would mean I couldn't then continue fostering as I don't have the space. I decided against having a second child for various reasons, fostering long term would really just be like having a second child, a much bigger commitment than short term fostering.
I also really enjoy the start of a new placement...the hectic first few weeks of welcoming a child into your home, getting to know them, the meetings, etc. that all take place at the beginning. I'm an ex-teacher now SAHM, and I see fostering as a job, working with children in my own home...I like the meetings with professionals/the training/etc. and I worry with a long term placement (particularly with the very lovely FC who's currently with us) that it wouldn't feel challenging/stimulating enough for me. I've only had four placements, I feel like I learn something with each one, and I don't want to give that side of things up just yet.
But then, it could be easier/calmer/less disruptive...?
I won't be surprised if we end up doing permanence at some point, but I think it will be several years away yet, and I think if it happens it will be because we as a family fall in love with a child who we then don't want to leave us.