But wasn't it in 2016-17 that there was already the blocksize war, resulting in the (unsuccessful) shitcoin cash hard fork? I think you don't have a new shitcoin cash in mind as a solution to the problem, and I would like to hear your idea.
I don't know if this is going a bit off topic in this thread but it is a thread I created, after all.
Bcash is a shitcoin not because it increased the block size but because it did it without any support and is essentially centralized. In fact most of the block size increase proposals were rejected because they were centralizing the system (eg. dynamic block size where miners decided its size, or a big block increase when we didn't need that much increase).
But we have already increased the bitcoin block size back in 2017 by a potential factor of 4 which in practice was a 1.5-1.7x increase. We've also followed that up with using the space more efficiently with the new change in 2021 which effectively increases capacity without increasing the block size.
These efforts are enough for the time being but eventually (maybe in a decade) there needs to be another significant change that would increase the size enough to satisfy the usage that includes second layer.
Is the adoption slow because of the lack of blockspace, or is blockspace not a problem because of the slow adoption?
The later. I don't think the adoption is being affected by blockspace. There are dozens of more important reasons why it is slow such as the volatility, FUD, being a new and "scary" technology,...
Even your example of the high fees was only a short term problem that didn't last past early 2018.
However, if we're talking about 100 million people who open and close several channels per year, and then imagine increasing 100 fold from there, we'll end up with GB blocks, and that's undesirable because it kills decentralization. As much as I'd like to see more blockspace for an increase in transaction numbers, it doesn't scale well to reach mass adoption.
You are overestimating the increase. Bitcoin network has been processing between 200k and 400k transactions per day. That means the capacity is currently at about 150 million transactions annually (only 100 million of it is was used in the past 365 days).
With more payment aggregation from big services and usage of new technologies (eg. using Taproot instead of legacy multisig) this can increase to 250 million. All with the current capacity without any protocol change.
To cover 100 million people opening and closing a couple of channels per year we won't need a 100x increase. Besides, with a hard fork the efficiency of the space that is being used will increase by a lot. With simple basic changes in such hard fork without changing the current potential 4 MB size we could increase it to 400 million tx/year.