Some companies utilize the rigid playing order well, but others do so poorly, seeking to hide lower path quality by forcing you to experience the lesser paths first. A classic example of this is Rui wa Tomo o Yobu as well as Comyu. In the former case, Rui's path is by far the weakest path in the game, and yet it is the first one you are forced to experience. The same goes for Benio's path in Comyu. This has a huge disadvantage, as it gives an impression that the game is lower quality than it actually is and leads to people dropping it without seeing the best parts. Ruitomo is still a top-quality game, but more than one person who has tried it at my suggestion has complained about Rui's path being so weak before dropping it.
On the other hand, Dies Irae does the same by enforcing that you play the game in the order of either Kasumi or Kei first, then Marie, than Rea. This actually works out ideally (especially since it links directly into the Shinzabansho canon), and it also allows you to ignore one or the other if you wish (Kasumi gets ignored the most often, incidentally, lol).
The most common use of Rigid Playing Order happens in chuunige as a genre. This is probably because the scenario directors and writers in these cases are far more likely to have a specific pathway to the finale than other genres. The methodology I came up with is to split heroines/paths into four tiers. I call these tiers the 'introductory path', the 'sub path', the 'main path' and the 'conclusion path'.
Introductory paths serve more as setting and character dynamic introductions more than anything else. They usually assiduously avoid presenting the 'hidden truths' of the setting and plot, while providing a truncated ending that deliberately falls short of what the reader would want. The aforementioned Benio and Rui paths, as well as the Anna path in Vermilion Bind of Blood all fall into this category.
Sub paths are a bit of an odd man out. For some reason, some VNs throw in random heroines and paths that have no real meaning for the story as a whole. Ayaya's path in Comyu and the 'normal paths' that sometimes appear in various games fall into this category.
Main paths are the most common type of path in plot-centric VNs. These paths have the quality of being conclusive when taken by themselves but do not resolve the plot's core conflict in a conclusive manner. Examples of such paths include Kei's path in Dies Irae, as well as most of the paths in Tasogare no Sinsemilla.
Conclusion paths are often represented as a true route, grand route, canon route, etc. The universal aspect of these paths is that they all resolve the core conflict of the plot in a conclusive manner, as well as tear the veil concealing most of the mysteries hidden in the other paths. They will often include variants of events that occurred in other paths that lead up to a grand conclusion, and there are often aspects of the plot that only make sense because you played the main paths prior to playing this type of path.