> grepping tcpdump output doesn't make sense given its extensive and well-documented expression syntax.

I dunno. If doesn't make sense in the world where everyone makes the most efficient pipelines for what they want; but in that world, they also always remember to use --line-buffered on grep when needed, and the line buffered output option for tcpdump.

In reality, for a short term thing, grepping on the grepable parts of the output can be easier than reviewing the docs to get the right filter to do what you really want. Ex, if you're dumping http requests and you want to see only lines that match some url, you can use grep. Might not catch everything, but usually I don't need to see everything.