Is there still a reason to buy camcorders?
It depends on the type of camcorder you get.  Most point and shoots use a cheap CMOS sensor.  The problem with this is that CMOS is read sequentially by line and results in an effect called screen tearing.  

Basically, as you pan quickly, the lines at the top of the frame are in a different position than in the bottom so that you end up with a jello like effect where vertical lines become diagonal.  A decent camcorder should use a CCD sensor which can capture an entire image at the same time and thus you get smooth panning.

While high end DSLRs have done a pretty good job at accounting for this issue by reading their sensor very quickly, low end consumer models, particularly of point and shoots, will have a substantial issue with this.  If money is tight and you can only get one, then, yes, a Point and Shoot should do a passable job for home video, but there is certainly a lot to be gained by using a camcorder of similar quality.

Another factor to consider is that there are often time limits on how long of videos can be captured without stopping on still cameras.  You can thank the European Union for this fantastic bit of idiocy because they decided to charge a significant tax on video cameras and defined them as anything that can shoot 30 minutes of video or more at a time.  Due to this, most camera manufacturers place a completely artificial limit of 29 minutes, 59 seconds on continuous recording from any still camera.  Some do make different versions outside of the EU, but others seem to be worried that it will make the EU come down on them if they only do it for the one model for the EU.