I like to think to security as a chain. The weaker link of the chain can compromise the whole system. So the whole thing become "preventing an unauthorized user from obtaining the root password".
As suggested by @DanMoulding the source of the software is also important and in the future probably official OS application stores will be the standard. Think about Play Store, Apple or Microsoft stores.
I think installation and distribution of covert malicious code is the
far more insidious problem. After all, in order to load bad code it s
got to first be installed on the system somewhere. More layers of
security are usually better, of course. The question is: is it worth
the cost?
In my opinion the answer is "it depends".
You can reduce the risk by adopting a set of security policies as suggested by @sleblanc. You can encrypt your file system (https://en.wikipedia.org/wiki/Linux_Unified_Key_Setup), use read-only file systems for the binaries or use a mechanism to sign and verify the binaries.
However whatever mechanism you use there is nothing you can do once the root access is obtained by an attacker. The signature verification tools can be replaced with a tampered version or just disabled and it doesn t really matter if the tools run in user-space or kernel-space once that the machine has been compromised (although the latter would be more secure of course).
So it would be nice if the Linux kernel could embeds a signature verification module and another security layer between the root user and the operating system.
For example this is the approach adopted on the recent macOS versions. Some file can t be modified (and sometimes read) even by the root account and there are restrictions also on the policies and kernel modules (e.g. only signed or authorized kext can be loaded on the system). Windows adopted more or less the same approach with AppLocker.