You could but the speeds are way slower than cable.
Depending on what tier of service you have with Time Warner, this hotspot will probably not be as fast but if most of the things you do on the internet are as described, then you may not notice the difference in speed all that much. People that do online gaming, stream lots of video and audio files, or do other things on the internet that require speed and/or good ping rates, may notice that this hotspot isn't a substitute for fast cable internet in the home setting.
And, Time Warner is good for those who consume large amount of data as I don't believe they are capping data consumption, correct? It does not sound as if you use large amounts of data so Time Warner like those who have habits similar to yours.
With this hotspot, you pay in advance for how much data you think you will use. You can be flexible in how you purchase service depending on your habits in consuming data. So yes, this may be a much better way for you to go than making Time Warner happy.