Blockchains can be made extremely scalable. You can break the problem into transaction volume (how many transactions can be processed on average per sec) and transaction velocity (how fast a particular transaction can be approved).
Transaction volume scalability results almost entirely from checking that the rules of the system have been followed i.e. that each block in the chain is valid. We now have very fast systems for recursively proving the validity of blockchains. For instance coda [0] requires very little space or computation (constant in the number of transactions) for a party to be convinced the blockchain is valid. Under such a system you could increase transaction volume by orders of magnitude.
Layer two protocols, such as the lightning network [1], offer near instant transaction velocity.
We can solve the scalability problems of blockchain. The thing that keeps me up at night is not scalability, it is user adoption beyond the use cases which Bitcoin already successfully fulfills.
[0]: https://codaprotocol.com/ [1]: https://lightning.network/