Lol. What company is going to run the second layers?
Do you even know what second layers are?
LN hubs, to be effective, have to be very big hubs with a lot of little customers connected to them with their small channels. In other words, banking nodes with a lot of capital to use as collateral on their customers' links, and inter-bank links. Big financial groups.
In the LN you have a huge economy of scale if you can put in a lot of collateral.
In fact, the LN will centralize even faster than the proof of work because the economies of scale are more important.
Can you cite the documentation that you must be referring to.
Banking nodes may exist in this future world obviously, but where is it that the system is reliant upon them.
Please provide your sources.
So as I stated, what company is going to run the second layers?
You are talking about Lightning Network. That is one proposed idea for second layers.