First, the median value would be more relevant for an analysis, because big hubs may be distorting the picture (the last time I checked the network structure it was a mix of the hub-and-spoke and the decentralized model, and there were definitively some big nodes with hundreds of channels).

I don't think that the average person needs more than 2 or 3 channels, often one alone will be sufficient.

Second, why should you open channels monthly if you only transact once a week? Remember that also average persons can receive money via LN, and that's where the potential lies. People would be most likely directly be connected with an exchange so they can "refill" easily, e.g. with their salary.

It is actually if you want to keep the network decentralized and secure, but I won't like to discuss that now. That has been discussed so many times, and it's not the topic of this thread.

It depends on "usage patterns", but we can at least do a basic estimation.

Let's say we define an "user persona" that wants to transact one time per day. He normally refills his channel via LN one or two times per month, but each 3 months he needs a "refunding" via an on-chain channel opening transaction.

This would give us approximately x50 scaling (up to roughly about 300-500 tx/s or 25-30 million tx/day): we have about 100 LN transactions each 3 months (3 x 30-31 plus LN refills) and need a new channel opening, whose size approximately doubles a "normal" 1-in-2-out transaction.

With channel factories and taking into account the same "usage pattern", we could reach about ten times more, so we get a potential of hundreds of millions of transactions per day.

However, we have to take into account that we need some space on the blockchain for 1) normal non-LN transactions, and 2) channel closing transactions in the case of scams. I would estimate roughly that this would takes to a capacity of a third to half of the number I wrote above.