The only thing a malicious host can do is to omit information, which can be mitigated simply by using more than one host, which is still cheaper than using a blockchain. You could have each signature include the previous one, which will allow anybody to verify that they have a complete prefix of the history. Host them on, say Imgur and Imgchest, and it would even be free, whereas hosting it on say the ethereum blockchain would cost about 10$ per image (Based on this: etherscan.io/gastracker#costTxAction. I’m lowballing my estimate. If its too high, please tell me by how much, and how you arrived at your number.)
In other words, even in the best case scenario, using the blockchain would only provide negligible benefits compared to much cheaper alternatives.