The weight of the rim basically boils down to the wheel's moment of intertia ("MOI") (and has zero to do with rolling resistance, with has to do with the rubber in the tire). You can think of MOI like you think of the bike's mass. The bike's mass adds inertia to the bike, which has to be overcome in order to accelerate it. Not to keep it moving, but to accelerate it. MOI is a wheel's version of mass, or inertia. MOI determines how much force it takes to accelerate a wheel up to the desired speed.

So yes, in theory, a higher MOI has to be overcome in order to accelerate the bike. The question is -- once the bike is moving along, just how big an effect does an MOI of "X" have versus an MOI of "Y" that is just a little bit higher? Most prognosticators just stop at the theoretical point and "conclude" that higher MOI is bad and that "weight at the rim is hugely important." But, they never have bothered to do the math.

When we do the math (which I am going to skip), we find that the range of MOI of various bike wheels will affect the average speed of a bike over a rolling course with various turns in a vanishingly small amount. So small that there exists no method of even measuring the effect in the real world. In other words, we can calculate the effect, but we couldn't actually observe it if we tried.

Conclusion: Fuggedaboutit.