The main goal of Napoleon's invasion of Russia was to beat their military in a decisive battle long before reaching Moscow, forcing Alexander to comply with the continental system - a European trade embargo created by Napoleon to weaken the British Empire who have been hostile toward France since long before the French revolution. Alexander signed this trade embargo during the treaty of Tilsit of 1807, and had been breaking the treaty for years by allowing trade with the British.
The Russians did intend to fight, and set up redoubts several times close to the invading army, but would always retreat when the Grande Armée approached. The military leadership in Russia was very indecisive, caught up in internal rivalries and disagreements. It didn't help that a large part of their military leadership was German. Aside from small skirmishes, they only gave battle once they were practically standing at the doorstep of Moscow, in the battle of Borodino.
The 400,000 dead soldiers died mostly to disease. Recent studies have found evidence of Borrelia Recurrentis which causes a form of relapsing fever. The western soldiers wouldn't have had any exposure to this bacteria before, so they were particularly weak to it. It was also exceptionally hot during the summer while they were invading (when the majority of soldiers died), which contributed to spread of disease and exhausting the horses. Disease and dying horses did way more damage to the Grande Armée than the Russian military did.
The campaign was a military disaster (though the people at home might not be aware, due to slow information flow and propaganda), but it was not without aim, and it was not obvious to anyone that 70% of the army would die to disease before a single major battle.
I appreciate that you at least didn't propagate the myth that Napoleon invaded in the winter, or that he lost because Kutuzov "outsmarted" him by giving him free passage to Moscow and burning it down.
> There’s a particular kind of person who can’t accept that story at face value
I would hope that the majority of readers here are taking the story with a huge pinch of salt. Napoleon's invasion of Russia is one of the most misunderstood events in modern history. Maybe that's why it's so popular to use it as an anecdote - because it can be molded to mean whatever you like, and people probably won't question you.