Just because they're the only ones with the consequences spelled out does not mean there shouldn't be consequences for other classes if you enforce the paladin's code.
Other classes are far more variable in their nature. That doesn't make them any less (or more) important.
Your point is true but incomplete.
Any DM can enforce devotion. Many (most?) DMs do not. In general, there's a fine line between telling a player how to play their character vs. enforcing the vague direction in the description of the (sub)class. A line that, rightly, many DMs would rather shy far away from.
The oaths however are, well, less vague if still not legalistic in definition, and are spelled out having mechanical repercussions for breaking them, which is something that a player is implicitly agreeing to by chosing the class. A DM can enforce those without stepping near the line.
Multiply this that often the (sub)class fluff in it's description is at odds with the setting. The guidelines for a generic Tempest cleric differ from a cleric of Zeus, and differ again from a cleric of Thor. Now it's even more muddled.
A DM can do this, but just like the Oaths are distilled to a couple of bullet points and there is buy in at class choice, that is the best way for a DM to put that sort of devotional restrictions on the other classes without straying too close to the "don't tell me how to play my character" line.
So just because it is possible for the DM to do so for any class, the default Paladin state is in a much better for a wide variety of DM to
realistically do so.