Why deliberately mismatch impedances in RF?
Design strategies do exist that involve intentionally mismatching stages. In my opinion, there are better ways to increase bandwidth, but mismatching is one method.

Say you're designing a 2-stage amp at 10ghz. Matching both stages at 10ghz might produce an amp with 0.5ghz skirts, resulting in gain from 9.5-10.5ghz, or 1ghz of bandwidth.

Now let's mismatch the two stages. Match one at 9.5ghz and one at 10.5ghz. Assume each stage still has 0.5ghz skirts. The overall amp will now have gain from 9.0-11ghz, or 2ghz of bandwidth.

The key here is, each stage has a gain curve that looks something like a bell curve. If two bell curves are offset, then added together, the result is a wider bell curve with a lower maximum.