Take a Honda Insight as an example - the car I have experience with this. If you're at 60 MPH and approach a hill, you use the hybrid battery to climb the hill. If you have the LRR tires, you barely need to apply any throttle to maintain that 60 MPH. If you have bigger, grippier, summer tires (which I did on mine), you had to give it say, 20% extra throttle to maintain the 60 MPH up hill. At the top of a big hill, with my LRR tires would still have 90% battery. With the grippy tires, it would be down to 50% or so. Gas mileage aside, that's another charge/discharge cycle and eventually the NiMH battery wears out much sooner I'd estimate from that.
The same problem occurs if you decide to drive 75 MPH instead of 55 MPH. You can hold 75 MPH with either tire, but the electric motor will drain the battery significantly when you're holding that speed, instead of relying on the ICE alone to gently cruise at 75. You have to give it more throttle, so you use more battery juice, at any speed where tire drag becomes noticeable. These LRR tires are designed to hold cruising speeds without using the battery. When you dip into more throttle %, it uses the battery and depletes it. It could even be bad for the battery because it'll be run low all the time. That happened with my Insight regularly. It also felt way quicker and more nimble with the stock tires. Yes it could hold higher cornering speeds with the grippy tires, but it was a major mismatch with the low power, small engine.
It could hold 70 MPH with very little throttle input (which in the case of the Insight puts it into Lean Burn mode and it gets 80+ MPG) w/ LRR, but barely hold 60 with the grippy tires and the same throttle, putting me into regular mode which gets 50 MPG. The gas mileage loss on top of that around town is still just one part of the puzzle, but I think the car is absolutely designed with the LRR tires in mind on EVs and hyrids. Disclaimer - My direct experience on these only applies to the Honda Insight.