This was once an excellent airline. During the 1980s Cathay Pacific accepted the Zimbabwe pilots licence, this was back in the days when they were very fussy. Ansett/Australian Airlines were very happy to employ Zimbabwean pilots after the 1989 strike. The Dubai Air Wing also has a few, as does Gulf Air and Emirates.
Now the airline reflects the country. When there are frequent power black outs because bills haven't been paid, when there have been cholera outbreaks because there isn't the money to import water treatment chemicals, what chance is there of the airline being first rate ?
Just because they fly in European airspace doesn't mean they are safe, remember they are banned from the USA and Australia. The list of airlines banned from Europe is only the worst of the worst, I'm sure Air Zimbabwe are better than the Congolese airlines listed.
Full flights would be mainly two reasons:
1. Lack of choice, with most other airlines having withdrawn.
2. Staff travelling to bring back goods to sell.
If the airline was under the supervision of a competent civil aviation authority such as that of Canada or New Zealand I would quite happily fly on them. At the moment who knows how bad things are ?