Guess and check (beast, as I understand it) requires some prior knowledge of the data format. I was imagining something that worked against entirely random data.

Yes. You can do simple things to data to make the basic byte-at-a-time attack hard to conduct. But a comparable amount of effort takes you to strong authenticated encryption. Virtually all systems that use ECB and have attacker-influenced plaintext are susceptible to the attack we're talking about.