This may be the fundamental problem with the DMG: back in 1st Edition that book contained a whole load of rules that were necessary for play. Since 2nd Edition the key rules have all been in the PHB, meaning that the DMG is needed only for the magic items and a handful of tables.
So maybe it's just a book that is struggling to justify its page count?
Sort of. The PHB is loaded down with a lot of things - races, classes, equipment, feats, spells, etc. I wouldn’t be adverse to putting magic items in the PHB, but would possibly strain the page count.
A lot of RPGs fit their main game into one book. D&D has only managed to do that once, and it got lambasted in 4E for the opposite with its PHB 1, 2, 3 and such. In many ways, D&D has too much stuff in it at its roots, and its hard to present it all in a small, slim set of books.
The one thing the PHB doesn’t really do is provide advice to play. It provides a couple springboard ideas for making this or that sort of character, but it doesn’t run you through what you need to know when you’re actually playing - like
how to use a character, dungeon delving tips, out-of-combat RP or many such things. Yeah, there’s plenty of other books on the market that can tell you these things, but the PHB is primarily mechanics, more encyclopedia than a “teach me to play” manual.
And to me, that’s what the true strength of a DMG would be - advice and tools for the DM. Sure, you could put magic items in the DMG, but what a
DM really needs is information of when and what to give out during the game, how to make new items and advice on what they should let PCs buy/build/sell. Same for monster & NPC creation - and how to use them, as well as a host of other aspects of the game, up to building an entire fantasy universe.
To me, the strength of the DMG should be in teaching someone how to put all these game elements together. Tables to inspire ideas and break down the components to make new stuff, and advice on how and when to use it all. It basically should be a D&D DIY kit book.