You're not going to be able to "effectively" propagate that transaction in 1 second to 7000 nodes with 3 neighbors. You would never have distributed consensus among those nodes. If user's can't get distributed consensus, then they will gravitate toward the subset of node(s) which has(have) the closest thing to it.
Why 1 sec, not 1 min?
Consensus among nodes is not required, it's perpendicular to consensus about ledger state.
I can't comment on the gravitation thing without knowing what reference strategy is being used in your scenario, I know at least one strategy that doesn't lead to fragmentation.
I assume you mean "why not 2000 transactions per minute?" Sergio says himself that it's only limited by the hardware deployed.
As there are no free-rides for transactions, the transaction/rate is limited by existent deployed computing power and electricity cost.
He then goes on to talk about the problems with increasing difficulty on transactions in this system;
By time-stamping every transaction, one could dynamically adapt the difficulty of the proof-of-work to achieve more fixed rate. But if the difficulty of a transactions depends on the difficulty of the parent transactions, then there may be incentives to choose old parent transactions instead of new ones to reduce the PoW required, if the current rate is over the fixed rate. Just to be sure Moore's law does [sic] permit spamming in the future, one could embed a re-targeting rule such that every 18 months the difficulty is doubled. It seems preferable that the last M transactions (such as M=10K) of a certain transaction vote on an increase or decrease of the difficulty of the following transactions (with small step changes). Then users could vote more freely on how the network should work without having any immediate benefit to bias voting. This is a similar problem as the current Bitcoin block-chain increase problem: only miners can vote, because user votes are prone to Sybil attacks. In DagCoin, every user can vote, as long as it transact.
I'd like to point out that in DagCoin, it is still only miners that vote. If you're a user that applies work on a transaction and broadcasts it, then you're a miner.
Work is a waste from the perspective of the miners. There is no incentive, or even a method to incentivize miners to do work on transactions in DagCoin. Competition would atrophy hashpower on the network in order to drive up transaction speeds, which is the product that the miner provides, users enjoy, and the only method of remuneration. Mining is just a cost that the miner wants to minimize.
This is just like if we removed the block size limit from Bitcoin and removed the subsidy.
That problem, the lack of funding for difficulty increases in order to slow down transaction speeds, isn't referenced in the white paper unless I missed it. So ultimately to get back to answering your original question "Why 1 sec, not 1 min?" the answer is I don't see any decentralized throttling mechanism that could actually work in DagCoin.