I don't think it's meant to compete with DIYers or small-time bloggers— that market is covered by wordpress.com's paid plans, and value-add services on top of shared hosting, like what SiteGround offers.
My sense is that WP Engine targets busy professionals who have first-hand experience of how much hassle a WP installation can be to maintain, people for whom downtime or being hacked has potentially a severe cost in terms of lost business, reputational damage, etc. The other way to look at it is that $300/mo sounds like a lot for "just a WP installation", but it's peanuts compared to hiring another person for your IT department.
That's fair - however I've been hosting some of these sites since 2014 on bare metal VPS with minimal issues (the occasional upgrade breaking a theme). A lot of WP issues come down to server settings / bad plugins over WP itself. I suspect WP Engine is largely charging that much to support any WP setup no matter how insecure.
Their platform actually actively tries to prevent you from being insecure. They limit what plugins you can install with an ever growing blacklist, and they try to handle as much of the performance stack as possible to reduce attack vectors. You don't like their caching layer? Too bad.
You're also paying for decent support tech's and support availability. I think to this day you can call and a human will pick up the phone. Tech's are well versed in the WordPress ecosystem and many are developers who can help you troubleshoot things at the code level, whereas with some budget webhost, they'll tell you to pound sand and hang up (albeit more politely).
That said, I think these "premium" WordPress hosts are purely for non-devs or devs with no time to provide their own support. If you're a developer, there is no reason to pay that premium to keep your blog online. If you want a more managed solution, use something like ServerPilot or SpinUp WP, or any number of other service that will provide a thin maintenance layer on top of any garden variety VPS provider.
My sense is that WP Engine targets busy professionals who have first-hand experience of how much hassle a WP installation can be to maintain, people for whom downtime or being hacked has potentially a severe cost in terms of lost business, reputational damage, etc. The other way to look at it is that $300/mo sounds like a lot for "just a WP installation", but it's peanuts compared to hiring another person for your IT department.