That's pretty much expected for large diameter low-profile tires which most cars come with these days. You could downsize to save a few bucks (but literally, that's all you're likely to be saving, nothing huge), but you will lose all the handling characteristics you've gotten used to, and the car will feel very sloppy (you may end up hating the way it feels after). I don't recommend it, but if you don't mind downgrading your Mazda3 to the performance level of the base model, it could work.
Check out the Tire Trends website. There are some not so expensive options available to you.
I'm guessing you are running stock 205/50VR17. You will want to stay with a "V" speed rating or higher. Your more affordable choices are:
Kumho Ectsa ASX / 205/50WR17 $159.67
Hankook Ventus K104 / 205/50YR17 (XL) $157.71
Kumho 712 Ecsta Supra / 205/50ZR17 $143.95
Sumitomo HTRZ II / 205/50WR17 $134.95
All are probably good choices, the only one with an "all-season" designation being the Kumho 712 Ecsta Supra. All-seasons are really meaningless anyway, and you should run separate dedicated winters (in which case, your downgrading to 15" steels for winter use might be acceptable for the typically slower winter speeds).