What are the advantages of the slide in semi-automatic pistol design?

A simple mechanism, rapid ejection of spent cartridge, rapid loading of fresh cartridge and some of the recoil energy is absorbed in driving the slide helping improve accuracy.

Purely speculation but I would imagine a huge advantage of the slide is that it seals much better than something like a P08, C96, frommer stop or their derivatives. As well as it would be much quicker to re-align sights with a slide seeing that many “slide-less” pistols used a kind of elbow extractor and ejected casings out of the top which would obstruct the shooters line of sight longer than is necessary where as most “exterior slide” pistols eject out of the side. However there are exceptions to both of these claims the most notable being the Desert eagle it seals well, extracts to the side, and is simple in design.

The biggest thing I think would be like mike said “exterior slide” pistols are generally much simpler and more intuitive in design and to minimize moving parts is to minimize the risk of failure when used in less than optimal conditions.