The argument seemed to be that it was impossible. it is obviously not.
the argument that D&D never really did it because there are only certain examples is, well, disingenuous.
And frankly, it would not matter whether it had never been done by anyone for any game -- it is still a better way to organize your monster book.
My point was that D&D had almost never done it and nearly every single 3pp monster book follows the same alphabetical listing that D&D has (almost) always done.
That even monsters by category wasn't even really done because there were always monsters in that category that weren't listed with that category. Remember when gnolls were type of giant? They were in 1e. Yet, never listed that way.
To be fair, the notion of monster "type" was a 3e invention because 3e added in the rules that all monsters of a given type shared the same base mechanics. HD, attack progression, that sort of thing. But, 5e doesn't do that. There's no such thing anymore of different HD sizes based on monster type - all monsters use D8's for HP. Attack progression is based on CR, not on monster type, nor do monsters of a given type get ability bonuses or penalties.
It doesn't really make any sense to list monsters by type since type doesn't have any mechanical impact. You could argue that listing by type makes it easier for DM's who are trying to find a type of monster to use in an adventure, but, then again, the same argument could be used for listing monsters by CR. After all, you're supposed to base your encounter budget on the CR of the monster, so, it doesn't make any sense to look up "ooze" and then have to hunt through oozes to find one that fits your CR. Why not look up CR 5 (for example) monsters and then find a monster that you like to use?
Then again, the question needs to be asked, how many people are using the Monster Manual by itself to design adventures? I certainly don't. Haven't in years. I am using a VTT, so I have everything searchable with numerous ways of searching - by type, by CR, alphabetically, combination, etc.
So, the question becomes, what is the easiest way for a DM? After all, many DM's are using published modules, which makes alphabetical listing the best - they have the monster name, they just want to find that. They don't want to have to know the monster type (which won't be listed in the module) in order to look up the monster. I'm not convinced that DM's are creating adventures the way you are
@Reynard. I think more DM's have tools that let them choose a monster - by CR, by type, by location - and need the Monster Manual to be a simple reference book.