You’re again talking in hypotheticals and ignoring the practical factors.
Around here, it’s usual for the utilities to limit residential services to 80A per phase (commercial properties can get a lot more).
So for a residential property you can literally get three times as much power by upgrading from single phase (which is common for small houses) to three phase (less common around here but available) due to this limit.
In theory I could just get a single phase service of three times the current, but in the real world the utility won’t give me that and makes me upgrade to three-phase.
This is by policy, since it helps balance the phases in the grid back to the local transformer, which the utility wants, so they also limit, for example, how much solar export you can do per phase for residential property - theoretically I should be able to export 15 kW on a single phase, but they don’t let me, so in the real world I am limited to 5 kW per phase, meaning I can only export 5 kW on single phase or 15 kW on three phase.
So in terms of pure electrical theory you are correct, but when thinking about real world policies of electrical utilities due to how power grids are designed, you do get a lot of benefit from three-phase.