Monologues are probably the toughest comedy bits to write because they are so restrictive. They have a very distinct set-up/punchline format that generally only work when the jokes are amazing. Monologues are rarely improvised and if they bomb, they bomb hard. This probably makes them the most hit or miss form of comedy of all.
So, when I see that just about every late night talk show has a monologue, it puzzles me. Why do they keep running these so-so segments. They don’t generally produce many laughs, even when the host is good, i.e. Conan O’Brien. Stephen Colbert used to have a great monologue but that was because he played a ridiculous character, instead of his real self. SNL’s Weekend Update is not that great, but it can be (i.e. the effectively blunt Seth Meyers, and the dry, awkward Norm MacDonald were quite hilarious as Weekend Update anchors).
My theory is that they keep monologues because they are the best bits to use in order for a host to make a point or share a stance. With Trump in the White House, monologues are used by hosts to criticize 45, with a mixed level of effectiveness.
Monologues work best when the writer focuses on structuring a story around a great punchline, or a hilariously bizarre story. Monologue jokes about dumb thieves tend to be funnier than diatribes against politicians.
This doesn’t mean you can’t write political jokes. Just make sure humour is your main priority.