Most end-users won't be acting as payment gateways, they'll all have private channels, so they won't appear in the routing graphs. The number of routing nodes would be many magnitude smaller than total number of LN users. It's working fine for now with growing adoption (1ml.com) and I believe it'll only get better with time.
Sure, but in order to accommodate more users you need more routing nodes. Exponential scaling is a funny thing- systems work perfectly right up until they catastrophically fail. That's why it's important to understand these kinds of problems ahead of time, which LN is determined not to do.
Look at it this way, if x = number of total users, routing nodes will grow O(log x), not O(c^x). The users can grow exponentially, the routing nodes won't because the marginal cost of processing an extra transaction from an end-user is very close to 0.
I thought the routing node was putting up some amount of Bitcoin per channel. Each channel would therefore have a non-zero cost (and each user requires a channel).
I would need to go back and refresh my understand as it's been quite a while since I read the LN whitepaper, much less kept abreast of developments in that space.
When you fund a channel, the Bitcoin is still yours, you're not giving it away.
With batched channel open/closes, it'll be super cheap to open and close channels. The only cost you'd pay is the opportunity cost if your counterparty isn't sending transactions, so you're not collecting routing fees. If that's the case, you can just close the channel if you need to fund another channel and don't have spare Bitcoin for it, but that's about it.
You've just outlined how the marginal cost that you originaly stated was near zero, is in fact quite a lot larger than zero (you can't open channels without locking up your node's Bitcoin). Also, each channel opening costs a Bitcoin L1 transaction fee (which is a lot larger than $0.01 and can only really grow from here).
Unless things have changed recently the big issue with LN is that it's fundamentally a centralizing force. The idea that everybody is going to open a million channels with every single counterparty (locking coins in the process) is ridiculous. Instead people would just open a couple of channels with big, centralized nodes but that's just Visa with cryptobabble on top.
Even if everyone had channels with the same, single central node it would have more guarantees than Visa does. The single central node could not just decide to keep everyone's money, as participants have the option to create an L1 transaction to withdraw funds if node they have a channel with misbehaves.
