Name a POS you want your Proof-of-Trust to apply to and we can look at that one. The above is the answer for Nxt. And which parts aren't true or you object to?
The general public, and even experienced Bitcoiners themselves, aren't very good at securing coins. This problem has been almost completely addressed for PoW by smartcard, hardware wallets for $30. With PoS, it's a different ballgame. You're required to keep coins online to stake, opening up the system to problems the general public will never be able to deal with unless they outsource that activity to someone else, aka a Bitcoin bank.
PoS systems that don't utilize coin age don't seem to provide benefit to small stakers at all. You have a combination of the small staker not being rewarded to stake factor, plus the general public tendency to outsource their staking to a Bitcoin bank since they don't want to deal with the risk and technology. This means a large movement to staking centralization and exchange centralization. It's really no different from Bitcoin PoW centralization. The exception is that circumstances that lead to double spend attacks for PoS coins, are much more dangerous long term for most PoS models than circumstances that lead to double spends for PoW coins.
I'm not particularly positive or negative on Bitshares, but DPOS, just like PoW, separates coin ownership from network control, so it doesn't have the above drawbacks where the general public is expected to jump through hoops that they aren't going to do, and will either not stake at all, which network security requires them to do, or will just outsource their staking to a Bitcoin bank, making it possibly more centralized than PoW.
I'm aware of NXT pool forging to try and combat the issues I've stated, which is, hilariously, almost like recreating PoW pool mining. It does have significantly less energy use than PoW, but once again, this is something that most or all NXT holders are expected to participate in to maintain network security, and the general public is just not going to do it. Once you start trying to fix the core issues of PoS, you start to run into issues that make it so the system might be too complex for the general public to use, since it seems to demand much more active participation than PoW, while also assuming everyone walking the planet is a combination of computer science and finance major.
The biggest issue of DPOS, is even if it's 100% positive your initial 101 delegate rollout can't and won't collude, how can you make a system to ensure that when they either stop delegating or die, that their replacements won't be colluding. Delegating as a DPOS participant should be a revenue stream, but maybe you will receive a more attractive, instant lump sum to sell out.
In summary, if Bitcoin PoW is ever found to be an inferior system to whatever PoS system emerges, Bitcoin PoW still has a large chance of beating it without even factoring in the network effect, just from being a much more simple and straightforward system.