I’ve got both US.Pro metric and imperial tap and die sets (both the 40pc versions), haven’t (touch wood) snapped one yet. They were only about £26 each.
Counter to Josh’s opinion, at least having the common sizes in a set means that when you f*** up, you have the tools to hand to fix it, not next weekend. And as long as you use at least 3 of them at some point you’ll probably get your moneys worth. If you do any DIY on your car they’re great for cleaning out old rusty threads or taking the excessive paint out of the threads in new parts.
Now for the bad news, bike mech hangers are 10x1mm thread, which is neither of the standard M10 threads. Pedal axles are 9/16, again not one you’ll find in most sets, and one side is reversed.
What you’ve linked to is a thread repair tool. Which is probably the correct tool for what you’re asking for, it’s designed to pull itself into an existing thread and straighten out the damaged metal. Whereas a Tap is designed to cut away metal to create new threads. You can use a tap to repair a thread, but it can also make a mess and cut out the wrong material and leave you with less thread than you had to begin with. Likewise a thread repairing tap might not be sharp enough to cut into really excessive paint or a badly distorted thread.