Why ambiguity is an indication of a healthy language
The truth is that the action of expressing something in any language has a cost. A cost in thinking how to put things into words and a cost in streaming these words out in oral speech or in writing.
So that just as everything else languages, tend to be simplified by their users. As Einstein would have put it, a language has to be "as simple as possible but not too simple".
The limit between the too simple and the just simple enough is precisely delineated by the proportion of ambiguity caused by every day simplifications.
The chicken example
Let's look at the verb to cook. To cook is an action verb that can be either transitive or intransitive:
1. I'm cooking the chicken
2. The chicken is cooking
The second sense came as the result of a simplification in English. Most Romance languages instead have two distinct verbs: one for the cook, the other for the food.
3. Je cuisine le poulet.
4. Le poulet est en train de cuire.
But of course, nobody will imagine that there is a chicken in the kitchen with an apron tied around its waist and keeping itself busy with pots and pans. In this case English is less precise but more efficient.
The dog example
The same thing can arguably been said about the sign you mention. There are actually many possible far-fetched interpretations of the sign:
Dogs must be carried on this escalator!
For instance, nobody imagines that the poster addresses stray dogs and requests them to dutifully wait for some passing-by biped to pick them up instead of boldly venturing alone on the escalator. Nor indeed that people without dogs should opt for the stairs. That is precisely why the joke is intended to be funny.
It is instead a characteristic of signs that they need to comply with stricter concision in order to condense as much meaning as possible in as few words as possible when they fall under the casual gaze of by-passers; and since concision is borderline to oversimplification the risk of ambiguity is higher in sign talk than in everyday talk, let alone scientific literature.
So in my opinion the sign is not ambiguous at all. I'd argue that you really have to think about it to come up with non straightforward interpretations.
Another dog example
Here is another example where the ambiguity is much more conspicuous. In this case the ambiguity comes from the fact that in English the pronoun "it" of a second clause usually refers to the subject of the first clause (in this case the dog).
This sign might need to be rephrased. The following sentence for instance is shorter and not ambiguous.
Dog poo must be put in a litter bin.
The striking thing is that we've actually come up with the same construction as your sign; viz. "Dogs... must...".