POS vs POW from the point of view of scalability of sharding.

This year was very rich in new technologies, many famous projects, for example, Ethereum, Polkadot and others, took the first steps towards the scalability of their networks.

Sharding is almost the only way to increase network scalability. It divides the nodes into groups, each of which is engaged in the creation/validation of only its own blocks. Typically, the more groups, the higher the overall network performance.

There are two ways to build charding:

POS

Sharding in the block chain with POS consensus is built with the use of the сentral chain. This can be in a clear form, when the main chain is pre-allocated (sometimes called a beacon) and several secondary chains are connected to it (sometimes called parachains). This can also be implicitly defined as a dynamic expansion of the number of shards, in which the central chain is essentially the first (zero) chain.

Why is this happening?

In POS, the construction of the correct chain of blocks is based on the deposit of money, and money is the numbers written in the correct sequence, in one sequence. So this is one chain and it is the central chain.

This means that the validation of chains of other chains requires the resources of the central chain. In it, to implement the functions of money, you need to support the processing of money transfers. It is even more loaded with cross-sharding transactions conducted through the central chain.

Obviously, the performance of a single chain is limited by physical hardware, so this design becomes a bottleneck and this limits the scalability of the network.

POW

The second way: without using the central chain.

All chains are equal, cross-chain transactions are sent directly between chains. This design is feasible for POW consensus when implementing merged mining (i.e. mining on the same hardware hashes for many chains at once). Since the block hash has only a mathematical (i.e. universal) nature, it can be checked in any chain. There is no need to support a central chain that would perform the function of money or any other operations. A hash calculated on one node can be used on many other nodes.

This is what makes it possible to build a network with theoretically unlimited performance.

Here you can draw an analogy with independent cities from ancient times, each city is an independent blockchain, and gold for settlements between them is a hash calculated on the power of the mining equipment of the entire network.

What do you think: is it true that a well-scalable blockchain cannot be built on the basis of POS?