While I really really hope no one would be that stupid as to risk a Kessler syndrome... I think it's really likely in a very specific situation:
A non-space-dominant power (so not Russia/China/USA) gets into a tiff with someone using satellites. This player does have access to at least the vaguest concept of a ballistic missile. They take said missile and program it to fly into space (as most beyond the tactical level do), and detonate.
Nuclear or not, they don't even have to hit the satellite, they just have to throw up shrapnel. Hell, you can replace most of the explosive warhead with ball bearings. It may not immediately take down a specific satellite but it's almost assured to fuck space up.
And in case it's not obvious, this seems like a very North Korean type thing to do. Their missiles aren't terribly reliable or accurate (so far), but good enough to get into space and ruin everyones day for a very long time there after. They have, what, a single satellite? [1] when everyone else has hundreds? Why not level the playing field and assure no one can use any of them - given enough time.
I'd be willing to be its in someones MAD playbook as well. It only takes a few hundred nukes to effectively end all life on earth, permanently. There are still 5,000 plus in both Russia and the US's stockpile [2], not to mention China, France and the UK has a couple hundred each. What do you do with some of those few thousand extra nukes? Detonate them in air and orbit to take out your Doomsday planes [3] and any potential orbital capabilities - just in case you survive.
But honestly, the Kessler Syndrome wouldn't really be a concern at that point since everything, including the roaches, would be a radioactive pile of glass.
[1] https://www.reuters.com/technology/space/north-koreas-first-...
[2] https://fas.org/initiative/status-world-nuclear-forces/
[3] https://en.wikipedia.org/wiki/Doomsday_plane