In my design, this was also true, but I realised it was exactly equivalent to buying stake in a PoS system; once you have your identity, you have a constant probability of producing a block, therefore a constant cost for attempting a double spend.
I was looking to design a system with equivalent security to a PoW chain but with improved confirmation times, so I stopped exploring at that point.
Maybe I didn't explain myself well enough - to create a new account requires POW but to maintain an existing account also requires POW (and this has to be done at the same time). The big difference with the approach to the normal POW approach is that the difficult work is not needed at every block (and nor can new accounts be created at every block).
This does provide an equivalent security in that the expense to mount a Sybil attack (in terms of POW) grows with every new account you add (so you'd need a lot of computing power to gain the majority of currently minting accounts).
If you look at the ideas of "weak blocks" (which are very likely to be added to Bitcoin next year) then you'll see that the approach I am taking is a bit more like that.
The confirmation times are sped up by the fact that most blocks only require low POW (and the minters can be preparing their difficult POW between the block where the information is sourced from and the block their POW tx needs to appear by).