How delicate/important is consistency?

Sometimes systems compromise inner consistency - recongnizable patterns throughout different mechanics, like a repetitive dice pool or a specific value range - in favor of other aspects of play; i.e. balance, simplicity, ease of use. For example, a long-ish roll that is otherwise perfectly simple and fine to use when characters perform ability checks might not be as optimal for situations where several tests will need to be rolled in quick succession, for example during combat - attack roll, damage roll, &c. - and so the system forgoes consistency to shorten tests during these sequences making them more fluid.

Sometimes this inconsistency impacts the game negatively, giving the mechanic in question the aspect of an afterthought, or a patch. But in certain situations it is possible that refusing to make room for these compromises hurts the system even more.

When is it okay to do so in your opinion? Where is the breaking point? Or even, does it bother you at all?