Would it be a bad idea to put lowering springs (pro-kit) on my Mazda3 sedan considering I drive around 420 miles a week? It would be for appearance purposes only. Should I be concerned about the accelerated wear and tear on other parts especially with the miles I will be putting on it.

Any changes to the wheel/tire size or suspension system will alter the engineered angle of the driveshaft between the transmission and differential. This will cause faster wear of the universal joints, and may effect component seals and bearings. "Everyone does it", but please be careful...

I don't think it would be a bad idea, so long as it is properly installed and the alignment can still be set to avoid excessive tire wear.
I think the amount of lowering that is available with that kit won't have a tremendous impact on driveline angle. That is after all front wheel drive and some driveline angle deflection is built in. But as rsain says, be careful. However does the work must have experience to do it right. Be sure to ask to save the O.E. components so that if you don't like the looks/ride, or if you want to eventually sell the car, you can have those parts on hand.

Your milage won't affect much any damage that can be made from lowering springs, what you need to watch more is the road conditions for the kit you use, depending on whether you use a kit you get from a place specializing in suspension vs. an all around car accesory place... it also depends on how much you lower your car, just make sure you watch out for imitation kits, the more the price the better the components, you don't want to get britle springs, because this will put more stress on your factory seals and bearings as Rsain2004 said... if you want to know my opinion, I would get adjustable suspension, it's a better ride and even though it will cost more it would probably save you money in the long run, as long as you treat your car right

By adjustable suspension, I mean airbags, airstruts, hydraulics, etc.

Obviously, Your ride quality will fall if you put just the springs on. Make sure you take your local area's road conditions into consideration.