If free loading and performance are the issue then why stop only on Zimbabwe? After all, we do have plenty of freeloaders and non performing actors in test status list.
Bangladesh makes a strong case, Windies as well despite rich legacy. Pakistan is not far behind. Likes of ireland and afghans hardly Play tests.
In case of Bangladesh and West Indies, I can't say that they are weaker than Nepal or Namibia, which is the case with Zimbabwe. If the BCB organizes a 5-match T20I series against Nepal, then we can expect Bangladesh to win the series easily by a margin of 4-1, or even 5-0. If ZC do the same, the results will be 2-3 or even 1-4 in favor of Nepal. Zimbabweans are playing it safe, by refusing to take on any of the associate teams (which actually preserves their T20I ranking).
Here I am not agreed with your observation about Zimbabwe vs Nepal even Zimbabwe is not performing good but still they could be done good, and I am sure result could be 2–3 in any team favor.
Zimbabwe is terrible in test format with their chances are high in white ball format because they are doing some work in this format, but their domestic setup in long format is never been good and ideal ICC needs to skip them from this and allowed to be play in other two formats which will be ok.
Now in test format difference of quality is widened between top 4 and others because mostly are doing not good work in test format which is surely not good while Australia, India, England and South Africa are on same level.