I should point out that I never saw grappling employed in any competitive matches. All of the sweep-and-grapple stuff happened in practice. Tai-atari and the tsuki are used very frequently and to great effect in shiai, of course.
The remove-your-left-hand-from-the-tsuka-and-wrap-it-around-the-other-guy's-shinai-and-disarm-him move sounds a little iffy from a "real technique" point of view, if for no other reason that in order to do so you will inevitably allow the opponent's shinai (supposedly a sword, right?) to come in contact with your body. Because modern kendo is a sport and practically nobody thinks of a shinai as a real sword, modern kendo tsuba-zeriai can be incredibly sloppy, with guys allowing supposedly razor-sharp swords to come into contact with their bodies (particularly the junction of the neck and shoulder), due to the nature of kendo tsuba-zeriai. The whole point of real tsuba-zeriai is to prevent that from happening. Unless you are heavily armored, tsuba-zeriai is potentially one of the most dangerous positions to be in, precisely because you are so close to the enemy's sword.
However, I knew some real magicians in tsuba-zeriai. A really good guy will approach it as a sort of "pushing hands" situation, and those guys with the touch are so sensitive that it feels like you are pushing on air, only to get whacked on the break before you know what is happening. A really good kendoka will be in tsuba-zeriai only for as long as it takes to set you up for a counter on the break. The bad kendoka will use it to try to manhandle the opponent or bulldoze him out of the ring a la a sumo-style "oshi-dashi", but this only works on people who are no good at tsuba-zeriai.
Also, on Japan vs. the US on the "roughness factor", my experience has been that kendo players who have no experience in Japan will assume that you are a violent sadist if you employ the tsuki too much or do anything that smacks of "real" violence. This seems to be simply a matter of whether the person has experience in Japan or not. I was once told at a US dojo not to employ the point in any way because of the danger of injury and resultant lawsuits. Frankly, I do not see how good kendo can be done without, at the very least, the implied threat of the tsuki or tai atari. Without this kendo is, well, no longer kendo. Kendo depends, ultimately, on having a strong kensen so that the enemy will be intimidated to the point of being unmanned and, thus, unable to attack. Without that, kendo kind of loses it's "point" so to speak. I have seen people completely defeated, and have myself been completely defeated, many times by an opponent with strong chudan no kamae, which always carries with it the threat of the tsuki.
However, within a dojo, the Japan-bred players will respond to a person based on the perceived ability of the opponent to "take it". At a US dojo, the (Japanese) sensei took me down with a hip throw once. I went head-over-teakettle and very nearly crashed into the chairs stacked up against the wall. I believe that he sensed he would have no problem doing this to me because of the way I was doing kendo. I make no claims to being any good, but Japanese kendo is very different from American kendo, and the Japanese-trained people know it and can tell who has trained in Japan and who has not, and, thus, where the boundaries are.
Also, riot squad police kendo is as to "normal" kendo, even in Japan, as pro sports are to amateur sports. Only the strongest players can aspire to being on the riot squad team, and their only job is to compete in and win the regional and national tournaments. If they lose too often, they are back to being regular omawari san, or beat cops.
In Kanazawa, the riot squad did nothing but practice kendo every day for 6 months out of the year, with mixed practice with "regular" kendo people on Sundays. The other 6 months of the year they had to do other work, so practice was reduced to 4-5 days a week. That is, they are true professional kendo men. They get paid to do it, and, as far as kendo is concerned, they are judged solely on their ability to win matches. Kind of like sumo, where a wrestler's rank depends on his tournament record.
And the Kanazawa squad I practiced with was, on a national level, no great shakes, regardless of how much better they were than I. In Yokohama, for example, the kidotai did nothing but practice kendo all year round. So it's just a matter of degree. But absolutely no other single kendo group in Japan is anywhere near as strong as the riot squad, unless it's the JDF guys.