As you increase confirmation time, you further inconvenience all users, while the attacker only has to find more victims.
Also, you assume total transaction fees is something large when the coin is actively used, but I can't see (or I overlooked it) how you incentivize each individual user to pay higher fees.
Yes, high confirmation times are bad for users. But in a crazy hypothetical world in which Bitcoin users switched to this system, it doesn't seem like transaction times would be significantly worse. Indeed, many transactions could be confirmed much faster, as the lag to one confirmation in Bitcoin with low fees is much higher than the lag to having a child transaction (or many) would be.
The PoW system provides security in the transition to (hypothetical) high usage. Paying higher fees is incentivized as child transactions gain more from descending from transactions with higher fees, and so confirmation is likely to be faster, whatever the confirmation metric.