A common misconception I see when people talk about future scaling of Bitcoin is the number of transactions per second you can get with any given blocksize. The argument typically goes something like "3 tps today, 5 tps with Segwit, 10 tps if you also double the blocksize". Which is technically accurate, and the only real ways to scale right now, but it does not mean that this is the best way to keep scaling beyond the near future. Even the maximum 256 MB block size supported by certain clients would add less than 1000 tps capacity, while at the same time increase the size of the blockchain by over 13 TB per year.
The smart way to scale Bitcoin usage for payment purposes at 1000 tps and beyond is, as most Bitcoin developers and many users have already realized, by using a network of bi-directional payment channels, such as those used by the Lightning Network – first envisioned by Joseph Poon and Thaddeus Dryja, this is currently an active development project headed by Rusty Russell. I have been watching this project since it was first announced back in 2015, and I am increasingly confident that this approach is in fact the only realistic way to scale Bitcoin to something that can be used daily by literally every single person on the planet – even to buy their coffee. And if your goal is having a global payment network usable for everyone, that is how high you have to aim.
It is important to emphasize that this is still on-chain scaling even if the payments are not individually inscribed on the blockchain. That is, we are not talking of "Bitcoin as a settlement network" but "Bitcoin as a globally-scaling payment network with a blockchain primarily used for settlement transactions". Any number of payments can pass back and forth through the payment channels, and after the initial funding transaction, nothing further is inscribed to the blockchain until the final outcome of a specific channel has been determined – at which point, the balance of the payment channel is settled on the blockchain. And while a channel may ideally simply remain open indefinitely, sending and receiving what is effectively the same coins an arbitrary number of times, realistically it will at some point always be closed and committed.
Not only does this mean that the vast majority of payments can safely happen without being inscribed individually; they will also happen near-instantaneously, only limited by network delay. Furthermore, the simple fact that the history of every individual payment is no longer public record adds significant fungibility to Bitcoin, as to the best of my knowledge, Lightning payments could only be tracked if they were intercepted live, if at all.
As such, the "scaling debate" should ideally be held based on the understanding that when Lighting is ready for use, even an avid Bitcoin user would typically only need to make at most a handful of blockchain transactions for payment purposes per year in order to open and close Lightning channels. If you were to limit the scope as such, it would largely reduce the debate to "what blockchain storage scaling do we need until Lightning is ready" and "what blockchain storage scaling does Lightning need to scale and operate safely" – neither of which I will attempt to address here.
However, before all of this can happen, what Lightning needs is Segwit. Non-malleable transactions are what make this possible, and if Segwit is not active by the time Lightning is ready to use it, that will be an incredible defeat for Bitcoin in general. There is still time, and it could happen as soon as with BIP148 on August 1st, or with BIP149 or similar BIP8-based activation possibly as early as November 16th if that fails. Alternatively, it could happen by throwing the miners a 2MB bone so they activate Segwit voluntarily with the SegWit2x/New York Agreement/"Barrycoin" proposal.
Ultimately, all of the alternatives have their own risks and significant detractors, but I hope that regardless of which of them end up gaining the most momentum, the rest of the ecosystem – that is, the miners, developers, economic actors and ultimately the end-users – will yield and move with them, so that any destructive chain splits can be avoided and Segwit can be activated as safely as possible.
tl;dr: Realistic future scaling absolutely relies on activating Segwit, so please do it.