A blockchain can scale but it would introduce an insane amount of complexity and it would add a significant performance overhead. All the blockchain's data would have to be split into x independent shards (e.g. mapped based on account address), then if (for example) an account sitting on Shard1 sends tokens to an account sitting on Shard2, the Shard2 block validators will need to receive and evaluate a state proof from Shard1 validators which proves that the transaction was recorded on Shard1 - Then those shard2 validators will credit the matching number of tokens into the account on Shard2. This approach is computationally expensive but it can scale to any number of TPS provided that you have enough shards (and nodes) to support it. It's also possible to do without state proofs since each validator could run as a cluster (across multiple processes or hosts) so a single validator could potentially have visibility over the entire sharded blockchain; each transaction would only affect 2 processes of each validator. An embarrassingly parallel solution is therefore possible; the more shards there are, the more idle capacity will be available to each validator (since each transaction only uses 2 out of x processes; where x also corresponds to the number of shards).

That said, I think the best solution is a multichain solution where each token is hosted on an independent blockchain and any token's relative value can be determined via on-chain data left behind by decentralized exchanges. Each blockchain only needs to have as few validators/nodes as are required to establish trust within the relevant community. If everyone within a specific community is happy to trust their financial records with a single person/node, then that's fine; but if they prefer to entrust a 10 person committee, they may want to setup a blockchain with 10 block validators... I would argue that a blockchain still makes sense even if the community just needs 1 block validator because it creates transparency in the sense that anyone can independently verify the financial records by running their own (non-validator) node; it makes it easy to see if the block validator tries to tamper with the records in any way.