The screws aren't made of swiss cheese, they're just not meant for your tool.
To open the EGR valve, or remove the IAC for that matter, purchase a JIS (Japanese Industrial Standard) bit set. All of the phillips screws on a Mazda are NOT technically phillips-head screws, they're JIS (Japanese Industrial Standard), which requires a wider, less pointy bit to avoid stripping out the head. JIS bits are almost square at the tip, so on these screws they'll engage the screw head completely. Use your normal, North American Phillips screwdriver, and it'll work only if the screw isn't fully torqued down, or isn't oxidized in place. Either way the JIS bits are a great investment of a few bucks to save a whole bunch of time working on Japanese vehicles (especially motorcycles).
I picked up mine at a local tool discounter- got a set that included and hex bits, and have never looked back.
I strongly suspect that many of the users reporting trouble a few thousand miles after cleaning the EGR are victims of this difference in screwdrivers. It won't let torque the screw down as far as it should go, and you'll get leaks.