In your first example, my intuition tells me if some elements are more important than others in away that's worth distinguishing with icons, it's better to think on providing easier access to them (priority at the top?) or hiding the rest.
There's 17 options there, where only 5 are deemed important.
The second example is bad for different reasons. There's no apparent rime or reason to the options other than "places you might want to check", no grouping and no priorisation. It would be a hard to parse with or without icons.
The brilliant thing about the first example is that differentiating "important" items with the icon actually allows multiple forms of categorizing items in the list, whereas your suggestions only allow one. The items in the list are grouped by topic, and important/common ones are highlighted with an icon. Hiding the less important options makes them needlessly harder to find if/when you do need them. Moving important items to the top breaks the topical grouping. In both cases, the application becomes less discoverable.
In the first example the items are grouped by topic (such as “printing”), which I think makes sense. When you go select a “frequent” action, it’s useful to see which “less frequent” but related actions exist nearby. And the icons not being all grouped together but being (partially) isolated actually helps in better recognizing them.
It’s from Microsoft Word ('97, I believe), by the way. A later version had “expandable” menus that by default only showed the most frequently used options, and on expansion (or by global setting) then also showed the other options. Many users didn’t like that, however, either because they missed that the menu could be expanded and thus didn’t find the item they were looking for, or because the expansion changed the relative locations of the items, meaning they were at an unexpected position depending on the expansion mode; or just because the expansion required an extra click.
I’m just noting this because Microsoft deemed the topical grouping of items within the menu important enough that they kept it, orthogonal to the expansion mechanism. And they doubled down on the grouping with the later ribbon interface — which I personally dislike because it’s not linearly greppable and feels jumbled, and they felt the need to give every item an icon there, whether memorable or not.
There was no way to get the default "short" menu right. Although conventional wisdom holds that "everyone only uses the same few features in Office," the reality is that people use an amazingly wide range of functionality. So, one person's ideal default "short" menu was exactly the wrong thing for someone else.
Hiding parts of the menu hinders discoverability when those options are needed, creates a need for one extra action to show all the available options, and messes with the users' spatial and muscle memory. This particular mistake was already made a quarter of a century ago, in Office 2000.
The easy access is that there is an icon next to them. Providing a collapsible menu just breaks muscle memory and adds an extra click to the other items. Microsoft tried this once.
There's 17 options there, where only 5 are deemed important.
The second example is bad for different reasons. There's no apparent rime or reason to the options other than "places you might want to check", no grouping and no priorisation. It would be a hard to parse with or without icons.