No, but it does require a serialization mechanism whose developers aren't actively hostile to it being used for information storage.
In other words, you can't use the bitcoin blockchain for this.
So if it isn't its own currency (and therefore pays no block reward) and you can't substitute the BTC blockchain, why should miners waste computing power on it?
I'm not sure that a block chain is required at all, but if it is, it's probably best to use the Bitcoin block chain. General timestamping with Bitcoin is incredibly useful, and it can't be done in other chains because the incentives aren't right. So it
should be allowed (with appropriate fees), and in practice it's probably difficult to prevent it.
why not make it easier on everyone and just allow say, 64 or 128 bytes of random data in a transaction?
That's already possible. OP_CHECKSIG. can be 33 to 120 bytes.
I also support a third transaction type for timestamp hash sized arbitrary data. There's no point not having one since you can already do it anyway. It would tell nodes they don't need to bother to index it.