But I strongly doubt it's illegal to cause thousands or even millions of computers to have random data in their browser caches, as long as no hacking takes plac

But I strongly doubt it's illegal to cause thousands or even millions of computers to have random data in their browser caches, as long as no hacking takes place? Just by padding files with dynamically generated random data, as I described above? We could write software to do this, and people can install it on their web servers, as a means of protest?