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Seb-wejem
You can definitely do away with the half races as well as any other race if it fits your setting, even a small change can alter the feel of a setting although it should be done as part of the setting rather than just not liking the race. I've come up with the bare bones of two settings, the first the players start as members of a tribe which limits the races to humans and also limits the classes. In the second, when developing it I started with a general history with elves, dwarves, and goblins. Humans came up from the south. A goblin shaman found a gemstone that enhanced the strongest goblins clans turning them into hobgoblins. A renegade elf that studied arcane magic left their homeland and taught humans wizardry in addition to fathering half-elven children. This leaves me with the following races in the current era: elf, dwarf, human, half-elf, goblin, and hobgoblin. This means that there are no gnomes (exceptions made for dual rapier wielding paladins), half-orcs, halflings, dragonborn, or tieflings.
They did that in Pathfinder 2 for the half-orc and half-elf, at least that was the set up at the start, I haven't checked the updates to the system to see if this is still the case.
I feel like the obvious solution to this problem would be to make half-whatever into subraces for humans. Base human stats are +1 to two different ability scores, and subraces provide abilities roughly equivalent to a Feat and a Skill, with variant human as the (ugh, these words feel really gross together, but there’s nothing for it...) pure human subrace.
They did that in Pathfinder 2 for the half-orc and half-elf, at least that was the set up at the start, I haven't checked the updates to the system to see if this is still the case.