The biggest advantage is that there is only one inlet into the block. For instance, a 5-station integrated valve block has one common inlet into the block and 5 outlets. If you compare with the alternative solution, which is mounting 5 inline valves next to each other, this gives 5 inlets and 5 outlets. The result is that you with a 5-station integrated block solution, 5 T-fittings are saved compared with a system with 5 inline valves. But not only the fitting cost is saved. Installation time is reduced too.
In addition, an integrated block solution takes up less space in comparison with the equivalent number of inline valves mounted next to each other. In applications where the space is limited this can be a real benefit.