In Nazi Germany Sturmabteilung or "Storm Division" was the paramilitary division of the Nazi party until it was replaced by the SS on the Night of Long Knives.
Some Neo-Nazis have kept up the language.
Stormfront is a popular Neo-Nazi website.
The Daily Stormer is another.
I don't follow Neo-Nazism but I am sure there are others.
So calling the riot a "Storming" is suggestive that it is an organized assault by Neo-Nazis.
I see your point, though.
The root reason for the violent riot at the Capitol last week was that many people have been lied to, and the lies are things that would incite people to fight. If you believed that America's democracy is no longer in place and has been replaced by a deep state dictatorship, you would probably fight against it yourself.
We must fight the beliefs at the source - stop the liars by making them liable for the damage they cause.
A lot of the mob on 1/6 probably really thought they were taking back the country from some corrupt Deep State and that Trump was this great guy who tried to fix the world, but has ben thwarted (although, saying all the non-Christian and non-Whites are not entitled to live here is not defensible). Like the lady who was shot, if you check her Twitter, she really bought into the whole QAnon brainwashing.
We have laws for actual harmful lies, such as falsely shouting "Fire!" in a crowded theater. But beyond that, it's a grey area, slippery slope, etc.
You have to take each case on an individual basis, meet a standard of proof, follow strong processes, convince a jury, survive appeals, so it’s not easy.
But it can handle the grey areas that worry you. And while we’ve had ample opportunity, it doesn’t look like we’ve gone down a slippery slope.