Hypothesis: a private group wants to create a 2ᵉ layer blockchain to facilitate its internal payments. The aim is to keep costs as low as possible, as well as energy and disk space consumption.
Important detail: the network is centralized. To transfer BTC, you just have to send your Bitcoin to the private group address, and specify your other address on the layer 2.
To save disk space, when nobody uses the network, the blockchain is simply deleted.
For energy consumption and costs, the first idea is to keep the mining difficulty at 1 forever. The second is to stop block generation, without disconnecting the network.
My question is: Is it possible to stop the block generation when mempool is empty?
If you're going to have a centralized system, and your proof-of-work is going to be meaningless, then why bother with a blockchain at all?
Just store the user balances in a traditional database. It will be faster, easier, and cheaper.
Blockchain exists for purposes where a traditional database is insufficient (distributed trustless systems).