This is not a post in support of a change in block size or for sidechains, I'm not qualified to take a side in that debate at all lol. What are the consequences of a block size increase and more specifically how it would be harmful for bitcoin's decentralization?
I think you hit on the answer earlier in your post: bigger blocks = a bigger blockchain = less people running full nodes = more centralization.
Somewhat humorously, BCH blocks never come close to getting filled and are on average much smaller than BTC blocks. BSV block size limit is even bigger and has even fewer transactions.
I think both the on- and off-chain scaling solutions are a much better approach than increasing the block size limit, for the very reason that its a bad idea to let the blockchain become exponentially larger. Right now its growing at a linear rate and it should be kept that way.
Of course there are those who absolutely insist on "staying true to Satoshi's white paper," which itself is not perfect and merely an outline for the idea of what went on to become bitcoin. I see increasing block size as merely the twiddling of an ancient parameter and rather a stagnant approach to a technology still largely under development.

Ironically here i am, weeks into syncing the blockchain and run a full node, but I'm barely halfway there (84g). I like bitcoin core solution, and the market likes bitcoin core as well regardless of what fork supporters say.
This is not "a war" though. It is about CHOICE. If you have a "better" idea, you are free to fork and see if others follow you. So far what others have proposed is clearly not good enough to take over the crown. Bitcoin as it is handled by the core team remains The King.
LN provides neat things like (true) decentralized exchange, you could theoretically directly exchange litecoin for bitcoin and back without using any web site (wallet to wallet). LN is optional, you may use it or not. Either way, providing this option is already offloading the on chain network enough for it to scale. Each shop could run its own LN node, and why not, a full Bitcoin node along it (and while you are at it an Electrum server pointed to your node).
Perhaps someone will sell some raspi pre-installed with everything so its plug and play and shops can have their solution ready, or same as there is a linux distro for "miners", a linux distro foe "nodes" (or the same distro could do both).
Anyway, enlarging blocks is dumb, I wish newbies stopped requesting that as a "solution" for a "problem" that is no more... Spend that energy pushing for faster wallet LN adoption...