You don't drop the unit for months, so it's not ambiguous in context.

It’s understood in context, that’s the point.

no it's not - it's assumed by maybe taking the most likely unit (year). But if the conversation is in hospital with your kid having emergency I guess doctor would appreciate to know if they will have to do surgery on 3 months child or 3 years kid.

If the doctor has trouble figuring out the difference between 3 months and years, there are bigger problems than specificity.

There are places specificity is necessary, and there are places the implicit assumptions people make are specific, and only need additional specification if the implication is violated. That's how language works - shortcuts everywhere, even with really important things, because people figure it out. There are also lots of examples of this biting people in the ass - it doesn't always work, even if most of the time, it does.

A 3 month old kid looks very different to a 3 year old kid.

and thats the exact point - you assume doctor see the kid instead of you calling doctor or doctor is getting briefed by emergency stuff.

Exactly! It makes sense in context.

As long as you construct a strawmen strict enough that can be no ambiguity, and refuses to acknowledge any context where it's not enough, yeah, it always make sense in context.