It has its uses: if the place is supposed to be in chaotic, confusing, impermanent state (like a dreamland, entrails of a beast, faceless unmapped mass of jungle or islands drifting in a void) it is easier to accept the quirks of procedural generation. It is good in strategies, when the terrain is randomized for each play. In character driven games (RPGs, platformers, shooters) it can provide more of surprise challenge in combat, where people have to think more on their feet than preplan the encounter. Arguably (see below) it makes multiple runs through the same area less monotonous.
Procedural generation is ok in tabletops as live DM can and will always enhance the experience of even the most random layout (such as Gardens of Ynn or Veins of the Earth) and it provides more of a canvas than a finished experience (also you don't mean to run through the same place that many times), but in videogames there is no DM, and the flaws become glaring.
Procedural generation eliminates the sense of genuine discovery: if everything is impermanent, nothing is important. There is no need to get familiar with the lay of the land, to learn its quirks - only the mastery over its smaller building blocks has benefit. The procedural place exists without history to it, without precise time-terrain imprint that might made it more than a sum of its parts. Without designer's specific intent the land has nothing to say about itself.
There is also no genuine surprise or secret to such places either, as even hidden chambers and significant landmarks are drawn from a limited pool and placed by the same algorithms that control anything else, remixed in the same way the wall tiles are. Even the moments of beauty which could be created by such procedures are diminished to me, as I know that those scenes are not specifically created to evoke this particular sense of wonder, but are just a random combination of numbers.
The unpredictability of procedural terrain wears off pretty quickly. Human perception has a good sense of pattern, and even without the knowledge of precise algorithm after a number of runs (smaller or bigger, depending on a quality of procedures) we start to distinguish the building blocks and get the general sense of procedures. And because the video games with procedural generation are so often designed for a multiple run-throughs (rogue-lites/-likes and not-Diablos especially), the monotony sets in sooner or later, negating one of few advantages the procedural generation initially has.
Procedural generation of a land can also be exploited. Bloodborne chalice dungeons have seeds that could be shared for easy farming of this or that resource. Even without a seed, if a layout is not to player's satisfaction, it usually could be easily 're-rolled' until more benevolent one is given, and all challenge of difficulty the procedural generation gives is mostly self-imposed as the player should decide to take whatever is rolled as it is rolled to actually limit/challenge themselves.
I think the main drawback of games with procedural generation is that they are so very often designed to be run through frequently and thus change often. If you take a game where procedural generation is only used once per run (such as the most wonderful Darkwood), there isn't that much dissonance between it and more handcrafted terrain.
In a way procedurally generated world could be how eldritch beings view our cosmos: made of limited building blocks, controlled by understandable algorithms, and devoid of specific history or intend.
