I don't know of any NN algorithms that match your definition entirely, and I have looked for them (previously and recently). Here are some papers that I think are close or in the direction that you are exploring.
Using theoretical models to analyze neural development (review)
An Instruction Language for Self-Construction in the Context of Neural Networks
Evolved neurogenesis and synaptogenesis for robotic control: the L-brain model
Modeling new neuron function: a history of using computational neuroscience to study adult neurogenesis (review)
The first two links are computational neuroscience papers that discuss relatively complex models of neurogenesis as it relates to neurodevelopment (rather than adult neurogenesis). Some of these models (inlcuding the second paper) do not even involve network activity, and, in their current form, likely none of them are capable or suited for solving practical problems. The third paper is probably closest to what you are looking for (but I don't have access), and the fourth is as its title suggests.
Many network models of neurogenesis focus on neurodevelopment. A fairly obvious conclusion seems to be that the reason for that is that neurogenesis' most important biological role is in neurodevelopment. I have thought alot about using neuroscience to derive NN algorithms that are both biologically plausible and functional, and have considered neurogenesis within that context. My present conclusion is that, outside of neuroevolution, neurogenesis is not currently an ideal focus for NN modeling, because its role in learning and computation seems to be mostly limited to a special case (the hippocampus) that is not well understood (despite its obvious importance).
In regards to cascade correlation, I suspect that a similar effect may be achieved in some biological NNs using only synaptogenesis and synaptic plasticity. Basically, if you have very many neurons and new learning is confined to a minimal number of synapses that are subsequently protected from future modification, then the effect might be the same as always confining new learning to newly-added neurons (as in CC-NN). Such a case would be consistent with these findings, for example. In such a model, it would not be biologically plausible, and perhaps not desirable, for each neuron to be connected with each neuron in the preceding and following layer, and thus a system for determining the pattern of exploratory connections would be required. To do that, one could draw from neurodevelopment models such as the above (in order to bias the targets of synaptogenesis, to seed initial connections of the network, or both) or, alternatively, try to derive algorithms that approximate observed connectivity patterns of biological networks.