Why matching shell trajectories would not save mixed-calibre battleships

Would early base-bleed shells with matched trajectories prevent HMS Dreadnought from adopting an all-big-gun battery?

Probably not; trajectory matching does not remove the ammunition complexity and manual fire-control workload of coordinating several calibres.

The counterfactual supplies sub-calibre base-bleed shells in about 1904 and assumes they solve the trajectory differences of mixed heavy batteries. That assumption still leaves several ammunition types for gunnery officers to coordinate. Before computer-assisted fire control, reconciling their range tables and ballistic calculations would impose a substantial manual workload. Coordinating that mixture across several ships compounds the difficulty. Dreadnought's simpler all-big-gun arrangement therefore retains its attraction even under the question's generous technical premise.