The advantages are several and too much obvious:

The first one is that it is allowed that the size of the basic header was always the same, and perfectly known.

The second one is that routers placed between a source address and a destination address, that is, in the route that a specific packet has to pass through, don't need to process even perform or understand any "following headers". It also means, for IPv4, the disadvantage that routers have to be more frequently updated to support any protocol new function, since it should be able to perform it, even when it hasn't to realize any respected function.

The third one is that there is no limit for the number of options that they support. In IPv4, it only can be supported options until a maximum of 40 bytes.