Speaking only from anecdotes and N=1.
I’d surprised if one were leaving any significant cycling-specific performance benefits on the table by doing only unilateral work.
There could some shortchanging on the other benefits of lifting (bone density, core strength and stability) by putting less total load on the shoulders and the spine. I would assume the same to be true for neuromuscular adaptations. I certainly feel different after bilateral lifts than I do after unilateral ones., even if working in the same set/rep ranges. I’d be surprised if any of the above was that big of a deal since, as you mentioned, you can still put a fair amount of weight on the shoulders even when working unilaterally.