"Get on with it" doesn't mean fix yourself, it means learn to live with it, find some way of achieving basic functioning in life in spite of your suffering. And yes, it's exactly what people with physical disabilities have to do too.
That looks different for everyone. It might mean medication, physical therapy of some kind either prescribed or private, "alternative therapies" as they're called, self-help measures, professional home carers or cleaners or meal services, psychotherapy/counselling, adaptations to both life/home/mindset. Basically whatever combination of things makes life liveable for the person.
I think there's a level of compassion fatigue in the world in general. IMO it's a combination of things. Firstly, being bombarded with bad news in the media all the time. I mean, can anyone remember the last time there wasn't some war somewhere that our country was getting involved in or a natural disaster occured that we were expected to feel sorry for? I honestly can't, because it never stops as far as I can see. And also because ordinary people have become unbearable needy, on the whole. I'm not sure why that is.
So many people's first go-to is to complain to friends and family about whatever is going on. And I do mean complain, they're not just mentioning it as part of conversation and a life update. They're leaning heavily on others, offloading all the time, wanting sympathy or needing jollying along, wanting practical help because they feel better not doing "it" alone, whatever "it" may be.
That's fine when it's ONE person in your life, doing it occasionally. It just doesn't work when it's everyone, seemingly all the time because there's always someone going through something. The people they're complaining to, those people have their own stuff going on.
If they're like me and don't talk about their health or any negative life circumstances (because it doesn't help, unless I'm talking to a medical professional/adjacent-person who can actually do something), people have no bloody idea what I'm already dealing with, before they start using me as an emotional dustbin for their frustrations with their own health or circumstances etc.
It's an unsustainable situation in the population in general. Exacerbated by a lack of decent, available and speedy interventions in healthcare of all kinds.
Personally I see -
"Everyone gets anxiety/depression"
"You've just got to snap yourself out of it/get on with things"
"Just do things that make you happy and you'll feel better"
"It's normal to be anxious, we all just have to get on with it"
as code for: "I have no further capacity to support you, so please stop going on about your problems".
Regardless of whether people understand or not (and a lot don't. They've had/known someone who's had eg mild depression and think all depression is like that). Regardless of whether they're being unreasonable or not. Regardless that we've all been told "sharing is caring ", "it's good to talk" and "it's ok not to be ok" - that all only applies up to a point. Whilst these are all true, it doesn't mean others have endless capacity to listen to someone's unhappiness or problems or anger or worries etc.
People are protecting their own energy. They don't want their own lives and mood dragged down by others misery. They don't want their own lives curtailed by people who can't keep up (which is why lots of disabled people have few/no friends IMO, ordinary people simply aren't willing to make the compromises to include them). There is a perception, true or otherwise, that people don't have enough downtime. And they're being choosy how they spend it.
Expecting a medical-level of understanding and support from friends/family/colleagues etc just isn't realistic. It's one of those things I believe the state has sneakily brainwashed us into thinking is true to attempt to relieve the burden on healthcare and the state. A kind of mentality of "talk to your friends, ask them for favours, you don't need us. See? You're still alive, so it must be adequate". When it isn't adequate and never will be.
So as much as it sucks, there really is no option other than to "get on with it" and find a way through.