I just got a Dot yesterday and I completely agree. Although I was walking toward the bathroom when I realized that I hadn't gone to pause and used the Dot for that. It worked well.
On my Echo Dot, if I try "Alexa, channel 06801 on Dish," Alexa says "Tuning to 06801 on Dish. I couldn't find that on Dish." and nothing happens.
If I try "Alexa, channel 68 on Dish," Alexa says "Tuning to 68 on Dish. It looks like you are not subscribed to this channel. To change your programming package, go to the Dish website." and nothing happens.