What prevented NXT from being distributed the same way bitcoins are? As Nxt's generating accounts receive now the transaction fees of the transactions included in the block they forged, it would be possible to add some new NXT to the balance of the generating account, incentivizing forging even more and distributing the currency in a better way.

Is there a technical reason why all NXT were distributed in the beginning instead of distributed over time?
If every block subsidizes the forger with extra coins (in addition to the fees) then bigger accounts become even bigger by following the compound interest curve. In a currency with selfish forgers most of the coins would be absorbed by very few accounts that would lead to centralization of the currency.

This was predicted (https://nxtforum.org/alternate-cryptocurrencies/dgex-assists-in-launch-of-a-new-crypto-fimk/msg58485/#msg58485) by me and proved in practice (http://forum.fimk.fi/index.php?topic=539.0) by FIMKRYPTO, which is a clone of Nxt with over-time distribution.

Regarding a PoW distribution, back in 2013, when Nxt was launched, PoW couldn't be used as a good distribution method because a CPU-friendly algorithm would give enormous advantage to botnet masters and a GPU-friendly one - to owners of GPU-based mining farms left after Bitcoin rise in 2012.