I think they have their time and place.
First and foremost, they are more involved as far as application and installment time vs. a screw-on filter. Plus, you'll need to carry more to make use of them (adapter ring, mounting plate, filters, filter pouch, etc). For travelling, they aren't exactly user friendly.
That all aside, I find they are great to have and use when you're in a situation that you can make use of them. I do mostly landscape style and I will take my LEE ND Grad filter any day of the week over a screw-on, reason being that the screw-on only allows you for half of your shot to be framed with the shaded portion whereas a square (in this case, rectangular) style allows you to move it up and down and the mount allows you to rotate accordingly.
I also like shooting longer shutter speeds making my Big Stopper and .6 ND valuable to me. Any water shots I've done have been improved through the use of these filters, same with sunset shots. Maybe it's just me, but I've also found that just in general I can use them to manipulate the lighting during the daytime and compensate some for harsh lighting.
I do think in many areas, screw-on filters are a better option, however, my main complaint is the amount you'd need and the cost of any good filters. I've learned my lesson about filters and you do get what you pay for. I like how with the LEE system I can buy one filter and whatever size adapters I need, but then I can use an array of filters with a variety of lenses.
In summary: it comes down to use, carrying and overall, expense.
For me...at least.