The problem of "lose/lose skills"

So, as an introduction, when I talk about a lose/lose skill, what I'm referring to is a skill/proficiency/ability/whatever that, as a player, feels bad to invest in *and* feels bad not to invest in. I think this is actually a really common problem in a very wide range of systems, but it's something I rarely see discussed, so I'm interested in how the sub feels about it.

Most often, I think the problem comes up with skills that are rarely relevant, but pretty awful not to be proficient in when they are. Languages are an example of this in many games: spending your character resources on learning some obscure language will often feel like a waste because it will rarely or possibly never come up, but when/if it does come up the entire rest of the party is pretty much excluded from the narrative unless they also invested in knowing the same obscure language. On aggregate, I don't think either of those options really feels good. Ride skills often present a similar conundrum: if you spend the vast majority of the game on foot, investing in ride usually doesn't feel very good; if you don't invest in ride, though, the rare parts of the game that are spent in the saddle are going to be a miserable slog.

In other words, I think there are a lot skills and abilities out there where if the GM tries to "shoot the monk," the rest of the table ends up catching strays. Obviously what specific skills-or-whatever will fall into this category depends a lot on the game's style and focus, but I think it's a problem that can come up in almost any game. Of course, the easiest solution is to just not include these skills in your system, but this is where they feel like a lose/lose from a design perspective, too: often there are clear verisimilitude/worldbuilding reasons why they should exist, and sometimes even specific mechanical reasons for them.

Is this an issue you've noticed in other systems, or in your own? What solutions or comprises were the best for your game or others that you've really enjoyed?

EDIT: Wow, this blew up much more than I was expecting. I probably don't have it in me to reply to all the comments, but I've really enjoyed reading all the different opinions and advice in here and wanted to just include a general thanks for everyone who's weighed in so far.