I have a photo printer and love the convenience. Yes, I do waste paper and ink, particularly when trying to get a good print of photos taken with a flash. However I find it more convenient than running to the store and quicker than ordering online.
There are two areas of concern though. First, if there are long times between printing, a printer may clog. It could clog beyond cleaning the printer head using the printer driver. That means you'll have to send the printer in for repair and, possibly, not be able to use any remaining ink in the cartridges.
Prints made professionally may last longer. As for actual supplies, the permanence of prints made at home depends on the type of ink and paper you use.
For example, here is some information about inexpensive ink cartridges and permanence ratings:
http://www.digicamhelp.com/inkjet-supplies/cheap-inkjet-cartridges.htm