I wouldn't say that Zimbabwe hardly gets chance to play international cricket. They are part of the ODI World Cup Super League, and therefore they are assured of 24 ODI matches this cycle. T20 matches are normally included along with the ODI tours. However, in test cricket they play fewer matches because they are not a part of the first division. On top of that, their players such as Blessing Muzarabani have taken part in county cricket recently.
Brendan Taylor has represented a number of franchises, apart from representing Nottinghamshire in county cricket.
My comparison was with Bangladesh. The number of games Bangladesh plays with A list teams if we compare it with the number of games Zimbabwe plays then Bangladesh will have the upper hand. I always felt that the Zimbabwe team lacks experience, they have good players who lack a lot of international exposure. If they are allowed to play more matches with A teams, they will gain more experience and improve their overall performance. Since countries like Zimbabwe do not generate a lot of revenue for ICC therefore they are left behind.