Hey Optic. Many kiters use their kites to ascend mountains. Like you said the slope can't be too steep, but kites can actually tackle pretty decent grades uphill. Using a lift is obviously the faster and more convient way up a resort hill, but if you're using a kite it allows you to ride up instead of sit around.
Using a kite at a ski resort that doesn't have a designated kite area (which some do actually) will most likely bring the ski patrol out and tell you to quit it. The big advantage of having a kite is where there aren't any lifts and the mountain is more or less uninhabited. Many videos that you see on youtube of people in the middle of no where riding up and down mountains are all based on this idea.
For the gear, if you pack right it won't be too bad. Freestyle (park type stuff I assume you meant) might be somewhat hindered, but backcountry riding and mountain riding won't be hard at all (the bags look like medium sized mountain day packs). If you practice you can get setup and take down times to under 5 minutes. I can elaborate on those techniques if you like.
Finally, also consider that some riders will crank uphill and then glide from the mountain top to the bottom
. Now that's something you can't do everyday!