So long as the TV supports the video file types you have there are no cons to using the TV as your player. May produce a better picture than a cheap media player. I also avoids any wifi issues you may have with a network drive.
If you connect a portable drive to a TV, you may need to get one with a power brick or go through a powered USB hub. I have run into quite a few TVs that can't power an external hard drive (even an SSD) on the TV USB power. Flash drives usually work though if you want to use one of those.