I don't think I've ridden that particular brand but I have ridden a couple (one flex, the other rigid). My experience was that on one bike especially I could feel the shaft wind up under power, which made me reluctant to apply full power (breaking someone's expensive shaft drive bike is a bad idea).
The Dutch article covers the main problems. To recap:
- very high torque meaning heavy parts are required, and shaft wind-up may be detectable to the rider.
- high torque also means accelerated wear for gears
- two pairs of gears means extra losses compared to a chain drive (the gear arrangement also increases losses compared to a chain because there's more metal sliding on metal under pressure)
- usually cannot change the gearing, what's designed in is what you get. Edit: I have seen internally geared hubs fitted so you can get multi-gear shaft drives, but you're still locked into that particular model hub gear (you can't swap the 3 speed hub gear for a 5 or 8 speed hub gear).
- unusual design makes servicing harder, and replacement parts may not be available.
The slop that the article complains about is not necessarily a problem by itself. But in that case it's an indication of premature wear, which is a problem. Some slop is inevitable, and old shaft drive bikes used to be designed with considerable slop and were quite wear-tolerant as a result. They traded efficiency for that, but it meant you got a bike that worked ok, and kept working ok for 20 years.
Another problem is that the parts that are wearing are not mass market parts, they're short-run precision made out gears using hard to work material (and they're cast then machined, which is expensive by itself). That translates to expensive. By comparison bicycle chain is almost a commodity - it's made by the kilometre by several manufacturers, so it's cheap and there is effective competition.
A common alternative is the full chain guards often seen on European bikes. That gives most of the benefit of the chain drive but using common bike parts in a way that any bike shop can service. It doesn't work as well, IMO, but a service interval of 10000km or so is better than an exposed chain and IMO a good compromise between cost and durability. As this question suggests a major benefit of chain oil is preservation rather than lubrication.