What do you need root for? Having root privileges exposed significantly increases attack surface and decreases security. You can use Shizuku on GrapheneOS if you want to, it requires adb and works on any Android ROM. Also, there is a way to get root on GrapheneOS, but I really donāt recommend it.
Root can be useful for plenty of reasons: there are many apps which use root access to increase privacy, customize the system, restrict apps, manage battery charging, enforce firewall for apps and system, block trackers, backup the system, etcā¦ I currently have 8 apps (if I donāt count all the lsposed modules) using the root privileges to do all of that but I also use it for other things like automation.
The only kind of security I want to have is privacy from my own apps installed on my system, something root privilege allow me to have. For the rest, I just donāt install any random program on my phone and I didnāt have any problem for years.
(and no, I canāt do any of that with shizuku or adb)
there are many apps which use root access to increase privacy
If you mean apps that allow you to restrict permissions of other Apps, thereās App Ops, it works with Shizuku
customize the system
You can do some customization with adb/Shizuku but for some things you might need root. But I would definitely value security over customizability.
manage battery charging
The OS can do that pretty well
enforce firewall for apps and system
GrapheneOS has a built-in firewall that you can use to block network access to any app on the system.
block trackers
You can do that with DNS services like NextDNS
backup the system
GrapheneOS has a built-in backup solution
When I was talking about ābattery chargingā, I meant using an app to limit the charging at a certain level: look for āaccaā or simple āaccā which is the module/daemon to manage that. You have to be root to do that and there is no way around. For the rest, sure, but thatās for GrapheneOS, I was talking in general, most ROM not having what GrapheneOS has and considering GrapheneOS is exclusively present on Pixel phones unfortunatelyā¦