It is possible, but absurd. Why more layers if layer 1 works fine just increasing the maximum block size? Bitcoin Cash did it and works flawlessly. Just try it.
> Bitcoin cash pays the price through centralisation
What centralization? If you are referring to the node implementations, it has several [0]: Bitcoin Node, Bitcoin Unlimited, Bitcoin Verde,... Bitcoin BTC has basically one: Bitcoin Core [1]. If you mean mining, it's the same as BTC, same mining algorithm, same miners.
> It can still only manage 100 transactions/second
True for now, but it's way more than it needs right now now [2]. But don't worry, this month upgrades to ABLA [3], and will be able to scale to as many tx/s as needed.
The increased block size increases the amount of storage required to run a full node (and also the bandwidth required to sync nodes). Even at just 100 tx/sec, you need 14x the storage of a bitcoin node (so around 10TB vs 700GB for bitcoin). That puts it out of reach for many people to run and so making it more centralised.
To compete with a payment rails like Visa and Mastercard, you'd need to increase that to 10000+ tx/sec, making running a node complete unfeasible for most people to run.
There's simply no such thing as a decentralised blockchain network with unlimited block-size. At some point if you want to remain decentralised, you have to create layer 2+ networks that can handle the smaller, high-bandwidth transactions, and so you may as well commit to that model now and focus on making the base layer as robust as possible.
Ultimately for a money to attract the most value, it needs to optimise for the very largest transactions, and offer the most robustness (i.e. most decentralisation). This is precisely what bitcoin has done.
If you mean a full non-mining nodes (which only a few people really need, merchants, exchanges, ...), read points 7 and 8 of the whitepaper. For full mining nodes, you need expensive specialized hardware anyway.
Non-mining nodes are just observers that do nothing good to the network. Is like going to war with popcorn as a weapon. Mining nodes are the only ones than can include transactions to a block.