The series of On Route stops along the highway system pretty much monopolized the coffee scene for Tims for those long distance drives. The rare Starbucks I can think of is the one they share on site at Webers on Hwy 11 which they opened in recent years.
Admittedly I'm a Webers goer whenever I head up that way. Although I did go off the beaten path this past summer and found a nice BBQ place called "The Shack" and coffee shop, Cafe Seoulista in Orillia.
Some of the Enroute locations have Starbucks. "Getting off the beaten path" isn't what people normally do now; fast in-and-out. There are all sorts of mom-and pops" in towns along the way but you have to search them out. Back in the day when travel was slower, the 'Weber's of the day' travel break was a sit-down meal at the old Sundial in Orillia or Haugen's on Hwy 12 near Port Perry (although it is still popular).
Keep in mind too that when Tim's was founded your bougie coffees like your Caramel Machiatto, your Strawberry Frappuccino and your No Fat, No whip, PSL never existed.
Back in the 60s and 70s you went for coffee and donuts. Thats it. Your coffee had milk and sugar nothing more. It wasn't fancy but it worked.
Tim's cant keep up because it was not their core business model. The public perception is that they are solely a coffee and donuts store. They have a monopoly in the rural areas because Starbucks cannot compete there. The business model for Starbucks is such that they need fresh product often which is not something you can do in Iqaluit, Yellowknife or Saskatoon. Imagine what those fancy drinks would cost in Yellowknife?
My point is Starbucks style drinks are what people want now and despite a feeble attempt to compete Tim's cant keep up. Iced Cappuccinos were just a stop gap. They cannot compare to the drinks starbucks has.
Perhaps moreso in urban areas. Small towns are less discerning; coffee.