This is fundamentally incorrect.
There's no way to just "push on" through real anxiety. The answer isn't to think through "what would happen if you made the call/stepped on the train" as you're asking people.
In the case of this call to GP, if no DH, she might have done it the next day. She might have made contact online.
Some people could never do it and the child might suffer. It's an illness with varying degrees of severity just like all illnesses.
People with anxiety KNOW there's not necessarily an identifiable harm or consequence, it's not logical.
You wouldn't say to a diabetic "well, try and regulate your blood sugar, it's not that serious".
Anxiety is an illness as well. People (temporarily) lose the ability to walk, talk, dress in some cases. It can lead to delusions, hallucinations; it can be a very powerful symptom.
Sure it probably is overused - by people who really are afraid to do something but could do it; and by people who aren't but can't be arsed to do something.
And by people feeling normal stress cos their body/brain is making an alert (check the passport, be prepared for the presentation). You're still wrong.
But the idea you're putting forward here is very regressive.
You don't have to have a diagnosis to be experiencing anxiety.