Lots of problems with 28GHz, or even 11 GHz.
The 11GHz band Docomo used and the 28 GHz band Samsung used is the range where DBS satellite signals are broadcast. As has been pointed out, water will attenuate these high frequency signals (that's why you will see "rain fade" as a heavy storm moves in, often before a single drop falls) But consider that satellite signals must have CLEAR line of sight. You can't install a dish aimed through a tree, the leaves of even a small tree will massively attenuate your signal.
Granted, the satellite is 22,000 miles further away than the cell tower, so the incoming signal is far far weaker, on the other hand you don't use a half meter dish on your phone as an antenna, either. So not only will getting a signal indoors present problems, even getting a signal standing up a tree could be an issue.
Yeah I know, you can install local boosters all over the place to avoid these problems, but who is going to pay for all that, just to get 5G data rates instead of 4G? The use case for 4G is pretty clear - you can stream video to your phone, and web pages download almost instantly (well, they would if it wasn't for all the back and forth in the protocol, but the actual download is a fraction of a second at 4G speed) What's the use case for 5G? Multiple 4K video streams to a device with a 4-6" screen? Ummm, sure....
The 2km spacing of the towers is also going to be a problem in the US. The reason why AT&T's 3G coverage sucked/sucks in the US was because GSM requires small cells and getting permission to put up towers all over the place has been a huge problem for them. Verizon's CDMA technology had a much larger cell size and thus they were able to cover an area with far fewer towers than AT&T required.
Between the inability to pass through anything and the tiny cells, 5G, at least in the form mentioned in the article, will never come to the US except in very limited areas. The most densely populated areas also have lots of tall buildings. If you're walking down the street and turn the corner you might lose the tower you were communicating with. Or if you step under a cloth awning. Or get behind a streetlight (high frequency signals are VERY directional)
I'm pretty skeptical we'll ever make use of such high frequency bands for mobile communication. Not that this will stop carriers from screaming FIVE G!!!! from the rooftops :)