Yeah, people do worse in real life. They pick up stuff of varying weights all the time at odd angles.
Also, I would say that your grip is going to be a bigger liability in those situations.
A trainer spending a year "strengthening your core" is called theft.
I'm a man and know more about mens standards, but if you can't back squat at least 1x your bodyweight you are probably pretty weak. Similar for deadlift. And these are just bare minimums. Most humans are FAR more capable than this. Maybe just multiply these by 0.5 for a women just based on genetic strength differences.
You can start with the bar if you want, you will eventually learn through experience based on your body your form for squatting. And the internet as well as being able to record yourself are readily available for practically everyone. Given that you can definitely learn the basics of form without necessary needing a trainer.
That's what we call a benefit. The reason those people are suddenly lifting their body weight? They've gotten stronger! Deadlift from day 1, people. Your back will thank you. If you're worried about it, ask someone to check your form at the gym (most people are friendly!), or just post it online (I did this when I first started lifting).
Being able to bend over and pick something heavy up off the ground is a pretty fundamentally important human movement.
And while progressive overload is needed, no one is going from the bar to massive weight overnight. Also, not everyone needs to have the goal of being a power lifter. Peter Attia talks about wanting his older clients to be able to a 45lb kettlebell squat, the average weight of a toddler grandkid for example.