Are you saying that your class came up with an antenna design that's about 100x cheaper than anything else out there today for leo satellites, and you didn't patent, nor start a company with it? Something is fishy about your story.
I’m not sure what you’re referring to when you say 100x cheaper. Googling “LEO satellite antenna” will result in plenty of hits that are well below $2000. As I said before, the $20 price point was for manufacturing of the antenna itself (micro strip antennas are very cheap, materials-wise) and so do not include any of the other auxiliary systems needed such as a radio transmitter, an amplifier, etc, although for LEO you dont need to shout very loud to be heard by the satellites.
I googled it, and didn't find any that were suitable for something anywhere near what SpaceX is doing. Please provide links if you know of some.
Not really. You'd be surprised how easy a LEO link budget is, the free space path loss isn't much more than a cell phone link.
I'm familiar with a link budget. That doesn't have anything to do with how much a phased array antenna costs.