They're scalable as long as you're able to provide Infrastructure as per their demand but providing that gigantic amount of computing power is not possible by an individual, that's where crowd-sourced distributed computing power came into picture which is what people call mining or technically verify the genuineness of a newly transacted block in a blockchain in the cryptocurrency world where people share their computing power to do the job.
It's not necessary that you'd always need public to do the mining. Initially, It depends on the type of blockchain network and number of transactions happened in the network.
Anyway, regardless of the network, eventually you would require more computing power to mine as the transactions grow.