If the long term intention of crypto-currencies is to be a primary choice for people to use instead of current financial systems (which it certainly SHOULD be, not just a speculators medium) then I wouldn't consider scaling to be solved until there is technology that can sustain > 10,000 tps....all day....every day...from the outset!
Kicking the can down the road with "Internet connections will be faster / mining more efficient / hard drives cheaper so it's not a problem right now!" isn't a solution. That's what we did with Bitcoin and look at that shit storm now!
That 10,000 tps is the low end of the scale, and allows all the current primaries such as VISA, Mastercard, Paypal, GooglePay etc and all C2C payments to migrate. When talking mass market, ease of use is paramount, so having multiple independent solutions that do say 1000 each isn't enough, consumers will not adopt it...it needs to be one platform ideally.
That's only the start though, with the advent of IoT, and the growth in electronic payments (VISA processing quantity is rising, MC's is too), that requirement increases further to > 25,000 tps in the next 5-10 years. If you then include the Asian block with the volume of such things like Alipay, it exceeds 200,000+ tps.
Segwit is not a solution, LN is not a solution (LN isn't even a good one....off chain? centralized 3rd parties? cmon!). Ultimately no block chain can scale to anything like that level no matter how many bags of tricks you bring without some form of centralization.
Confirmation or settlement time is paramount too, no one wants to wait around for transactions to process for long periods of time. IMO the settlement time of a network poised to be a replacement of the incumbents needs to settle in 10 seconds or less and should be equivalent in security to at least 2 BTC confirms at present, at least for priority payments such as Point of Sale.
Fast confirmation is possible to a degree on a block chain if the size of the blocks is low, but once volume increases it becomes harder to maintain it.
If you're wondering why the above isn't possible on a block chain, simply its due to the architecture of a block chain requiring synchronicity of state at all times... therefore CAP theorem and speed of light are NOT a block chain's friend.
If you claim a block chain can do the above sufficiently, well....you're wrong.
This is the holy grail of posts on this website. No block chain will ever be able to do what people envision (as you stated so eloquently in this post).
PoW, PoS, PoW+PoS, PoI , 10 min block, 2.5 min block, 10 second block, 1 MB, 5 MB, 10 MB ... none of that matters
I have no dog in this fight, as I'm a simple observer, but check out IOTA.
www.iota.org