You are talking about a central system service, so no, you won't be able to remove it without root. And I'd be wary of doing so anyway - you'd have to be very sure that nothing depends on it (both apps you have installed, because some apps do use accessibility options to provide functionality, and other system functions. It's not uncommon in computer operating systems, not just Android, for some functionality to have the same basis as the accessibility options and hence be provided by the accessibility service - both my phone and my laptop have a few apps that work this way).
But the key point is that this is a system service, part of the operating system (not a manufacturer-specific add-on either). I'm cautious about permissions, but there's a point at which if you aren't comfortable with the operating system having this access you'll never be comfortable with a smartphone. Of course given how much phones are used for tracking their users a degree of discomfort is healthy, but this wouldn't be the thing that I'm most wary of.