Well, they usually are not distinct certifications. The various authorities have bilateral agreements as to the equivalency of each others' certification standards - based on both the underlying ICAo standards and also commonality of the specific standards themselves, so usually the additional effort to certify in the second or third jurisdiction is minimal. For example, my own company certifies with Transport Canada as lead authority, because they are our national authority. But EASA and FAA certification usually follows just a month or two later, and the incremental work is less than 10% in terms of flight testing; the other authorities do a spot check validation rather than a full certification exercise. TCCA reciprocate for FAA and EASA certified aiurcraft.
Why do it? Well, if I want to register an aircraft in country X, then it has to be approved for a Cof A by that country. That means passing that country's certification rules. And why do i want to register locally? Sometimes tax reasons, sometimes a requirement that I register locally. It even applies to the smaller countries. if I want to register in Bermuda for tax reasons, the Bermudan authorities need to be able to give me a C of A, and at least tick the boxes toi say I have met some kind of requirement.
Again, at my company, we usually have one or more exercises every year to 'validate' a certification for a new country that has its own wrinkles on the basic FAR/CS/TC rules, because enough customers exist in that country to make it worth getting the approval.
One single certification and hence one single set of rules is the holy grail of "harmonization" of cert requirements. But cert requirements are ultimately laws, and laws are made by politicians. So until you get all the politicians to agree, there'll always be some rule that is important to one country that the others don't want. (For example, Canada has some specific concerns about cold weather operations, not surprisingly; FAA and EASA don't put the same emphasis on these concerns)