Every tire has at least one downside:
- Construction quality (holding air, staying in balance, not degrading)
- Ride quality
- Noise
- Treadwear
- Dry traction
- Wet traction
- Rolling resistance
- On-center feel
- Continued performance from brand new down to the wear bars
All of the above are crucial to how safe and/or tolerable the car is to drive.
More expensive tires have fewer and/or less severe disadvantages. Less expensive tires often have at least one Achilles heel -- they might be good overall, but there's that one thing (or more) about them that is just awful.
This isn't like a car, where you have to pay thousands of dollars for a small advantage in performance or comfort. The difference between the least expensive and the most expensive tire in any given class seems like a big deal up front, but when you spread it out over months or years it's really not that big a deal. Meanwhile, what you get for that money can mean the difference between a decent car and a great one -- or it could even save your life and someone else's. I've never seen a case in which it wasn't worth it.
There are exceptions, of course. Some tires are just overpriced, like the stockers for my car. But I only say they're overpriced because I can get Michelins (which, as I understand, are comprehensively better) for a tad less money.
There are plenty of reasons not to go with a first-tier manufacturer for your car, your fridge, your TV, or your home stereo. The only reason not to go with tier 1 for tires is if you constantly blow them out before they reach middle age.