It's feasible to make a high speed internet satellite communication system. People have done it. Making it affordable is something nobody has even come close to achieving, and the approach they proposed was one that has already failed spectacularly once.
I think this is Google sending out feelers about a possible technology, but I don't think it will ever materialize.
I'm serious about the cost. Check out the rates for BGAN, and don't forget this is on top of buying several hundred dollars of satellite gear in the first place:
$4.50 per Megabyte. A funny cat GIF could cost you $15-20 easily. And BGAN is popular because it is cheaper than most alternatives.
Oh, and if you want, you could in fact use Iridium today. The constellation is still up there and people are still using it. You can expect a data rate of around 4800 bps (although I experienced data rates as low as 900bps frequently while using it) and it will hiccup every time it has to do a handoff (newer modems might be better at this). It costs something like $7 a minute. You can also use it as a phone service (the original purpose in fact), but it makes you sound like a robot and the delay is just long enough to be noticeable and annoying. It is truly the ISP of last resort.