Actually there are some subtle flaws possible with PoW schemes where you can't easily tell what any given leaf is for, especially if you want to define total difficulty such that subsequent miners add to it regardless of what chain they are mining: PoW reuse and PoW hiding. Basically you don't want it to be possible to use a PoW twice, and you also don't want to make it easy to hide the chain that was worked on and reveal it after the fact.
The latter problem essentially comes down to the fact that you don't want it to be possible for a lot of work to be done on a chain - adding blocks to it - without that being public knowledge. PoW schemes don't have that problem generally because they assume no on entity controls more than 50% of the hashing power. The chain can only be extended by being public so lots of people work on it.
But with a timestamping scheme the whole point is to let the chain be extended by people who
aren't involved with your currency, and may not even know it exists. But lets jump to problem #1 again for a second.
If your timestamping scheme's merkle tree allows the block hash for the chain to be placed anywhere in the tree's roots someone can mine two blocks at once. This is bad because no node can know which of the two blocks is correct, and making one of the blocks preferred by a rule like "lowest block hash wins at a given height" causes convergence problems. (you can withhold a particularly good solution and release it after someone finds another block, making the best block tip your block again and resetting the confirmation)
The former problem has an (attempted) solution in the
merged mining specification by having a system of slots for each alt-coin mined, and making the order of those slots deterministic. Unfortunately it's broken and doesn't work. FWIW this actually got implemented due to a slightly different and more serious problem: early attempts at merge mining still defined the block hash as the hash of the
alt-chain's header, so you could mine multiple blocks in one go. A better merge mining system re: PoW re-use would be some kind of defined path, basically from the tip of the tree "go left, then right, then right, then left etc." in a long sequence, and provided the path follows the right sequence it's valid, but that's maybe a little lower level than the overall ideas I'm describing here.
Going back to problem #2, lets suppose chain height was defined as increasing for every "timestamp" block added to the overall chain. If #1 isn't solved, you can just mine the occasional block here and there, hold that back, and then suddenly tell the world "Hey! Look at this really long chain I have!", deceiving clients into thinking they're on a valid chain. It's not an insurmountable problem - carefully chosen rules to chose what the best block may be solve it - but it makes SPV clients quite a bit more complex and the whole issue needs to be very carefully considered. AFAIK no-one has done the research required to do this properly.
I know I haven't explained the issue fully, but that's kinda my point: even after seven paragraphs of text I'm not even close to talking about all the subtle issues and no-one is really sure if there are even more subtle problems inherent in these ideas. It'd be nice if some alt-coins explored them, but that's a lot more work than pump-n-dump schemes...