How scalable is a Blockchain-based system? This question as stated above is a bit vague, but let me make it a bit more clear:

Recently, I have seen many services pop up that state that they are secure, fault-tolerant, trustless and scalable because they use a blockchain (often the Bitcoin block chain, the Ethereum blockchain or one of many other or proprietary 'block chains') to store the important parts of the data the services handle.

Now, security and fault-tolerancy I can understand, because (after a few more blocks are mined):


Everone can check the integrity and authenticity of a transaction because ECDSA-signatures are used, giving the system non-repudiation as property.
Everyone has a copy of the block chain so-far stored locally, making it virtually impossible to destroy data. ❦
it becomes virtually impossible to alter a previously-made transaction, because this means that all hashes of blocks after that need to be re-calculated.


Now, because of ❦, the system is also trustless, assuming everyone can read/understand the data from the blockchain directly (i.e. the service's interface to the block chain is released as open-source software). This is where quite a few services claims fall short.

However, the final claim: scalability. I cannot understand how a system can be scalable if it involves the copying of all the (trans)actions its users did to all other users' computers (again, this follows from ❦): It will 
both take a lot of time and a lot of disk space to do all this copying, and at some point a physical limit will be reached in which more actions are taken than can be written to the blockchain and in which it takes longer to catch up to the head of the chain than that new transactions appear. In both cases the system will break down (?).

I can see only one ways to resolve this, which is to use 'light wallets' for the end users, in which case the system is no longer trustless, as these users need to trust that the parties they talk with are honest in the version of the block chain they show, so this breaks the other claims.

I don't believe all of the systems that state 'Blockchain inside' use this approach.

So my question: What other techniques are used to make a Blockchain-based system more scalable, and how scalable (in transaction throughput) is a system as a result?
Blockchains are not really scalable. For the most security, blockchains need to be replicated on as many devices as possible. Those devices are full nodes and must download and verify every single block and transaction. In order to increase the number of transactions, transactions have to become smaller and blocks have to become bigger. Unfortunately increasing block size and transaction capacity will result in more resources required to verify and store them all.