Root access and unlocked bootloader are very different things. Many apps need root access to work, and having an unlocked bootloader won't help. On the other hand, installing another ROM requires an unlocked bootloader, but having root access won't help with it.

you can't have root access without unlocked bootloader, simple as that

I can access everything as root from recovery with unlocked bootloader without having actual root in system, root just make it more convenient after proper boot

> you can't have root access without unlocked bootloader, simple as that

Various EoP exploits for the kernel begs to differ. That said, even though your statement is broadly true, conflating unlocked bootloader and root access in the OS under an umbrella term of "root" is still sloppy terminology. The terms are related, but don't mean the same thing. For instance, many x86 PCs essentially have locked bootloaders by default (secure boot), but you can still get root access on them because the operating system explicitly allows it.