Now I can pay a fee of 50 sats/vbyte to open a channel, and then buy 100 coffees through that channel before I need to close it. In this scenario I have saved money on fees by paying 0.5 sats/vbyte per each of my 100 transactions, but at the same time I have paid 10x what I would usually pay for the block space.
But you will still need to pay on average 1$ for each coffee purchase to conitribute enough to the network.
So you either lock in 1000 coffee purchases or we, hmm, how do I say this, we increase the number of possible transactions in a block, by increasing something... something.. not width, not length, but , maybe size?

You are really not using LN optimally if you are opening a channel and making a series of one-way transactions. The optimal way to use LN is to open a channel with some value of coin on your side of the channel, to spend some money via various transactions (perhaps "everyday" transactions such as buying coffee), *
and* receiving coin via payments for things such as your salary and/or goods/services. So you may open a channel with enough money to pay for 20 coffees, but are able, over a period of time, to buy hundreds of cups of coffee because you continuously receive (a portion of) your salary to the channel.
So someone opening a LN channel can reasonably pay a high fee compared to the size of the channel, if they are confident their counterparty will not give them a reason to close the channel quickly. This will allow miners to receive a larger amount of coin on a per-block basis, even if the maximum block size is not increased.