Do the newest computers still have ROM?
Yes, or maybe no, depending on your definitions. Commonly some small 8-pin SPI NOR-Flash ROM is used, for example my slightly older motherboard has a W25Q64FV. This replaces the older non-flash based EEPROM technology since Flash is cheaper, but it fills the same role, and often the flash versions are still called EEPROM. Since it's Flash memory, you could call that &quot;not ROM&quot;, if your definition of ROM excludes Flash.
An other problem with relying on a disk is that a disk cannot come pre-programmed correctly. It needs to contain code specific for the motherboard, and be pre-loaded with microcode for the various diffent CPU models supported by that motherboard (which is why recently AMD motherboard manufacturers had some trouble). A disk does not know which motherboard it ends up in, so it cannot fill this role.