The evolution of MSP started in the 1990s with the emergence of application service providers (ASPs) who helped pave the way for remote support for IT infrastructure. From the initial focus of remote monitoring and management of servers and networks, the scope of an MSP's services expanded to include mobile device management, managed security, remote firewall administration and security-as-a-service, and managed print services. Around 2005, Karl W. Palachuk, Amy Luby (Founder of Managed Service Provider Services Network acquired by High Street Technology Ventures), and Erick Simpson (Managed Services Provider University) were the first advocates and the pioneers of the managed services business model.
In terms of MSSPs future, I think that we're only now seeing the tip of the iceberg. The reality is that cybersecurity is becoming increasingly more complex, expensive, and essential. I've covered a number of these angles in a recent article https://silentbreach.com/blog_article.php?post=33 . The upshot is that, as you've correctly pointed out, MSSPs are just much more efficient than a typical in-house IT team.
Backup and Disaster Recovery (BDR)—a combination of data backup and disaster-recovery solutions that works cohesively to ensure an organization's critical business functions will continue to operate despite serious incidents or disasters that might otherwise have interrupted them, or will be recovered to an operational state within a reasonably short period.