Sure, in some contexts you would know that the carry flag was set or clear (depending on what you needed), and it was common to take advantage of that and not add an explicit clc or sec, although you better comment the assumption/dependency on the preceding code.

However the 6502 doesn't support reg-reg ALU operations, only reg-mem, so there simply is no xor a,a or sbc a,a support. You'd either have to do the explicit lda #0, or maybe use txa/tya if there was a free zero to be had.