... So if people started to use it massively for big payments a more centralized structure could emerge. I would prefer instead to use sidechains for mid-to-large payments.
Why wouldn´t you use the main blockchain for mid-to-large payments? After all the main blockchain
will work just fine after the Lightning Network is widely adopted and you can still decide to use it
instead of making a transaction using the Lightning Network.
Using a sidechain seems unnecessary if you can simply continue to use the main layer.
For mid-to-large payments the fees are negligible as a percentage anyway.