I disagree with some of this, sometimes anxiety can be irrational that's true, however a number of times is has its basis physical or psychological changes / events.
Worrying the sky might fall on your head is irrational, worrying about being struck by lightning if caught in a lightning storm, not so much.
Anxiety very often has a basis in the rational, the anxiety can magnify the rational so it becomes irrational.
You use fear in your example, so is it irrational to be scared of snakes? No, why because snakes can bite and some are highly venomous. Is it irrational to be fearful of a snake hiding under you bed in the Uk, yes of course, would that fear be irrational say in rural Tanzania? No of course not. But you can't just switch off millennia of instinct. If you live without fear, then you'll be at much greater risk of putting yourself in danger. Look at toddlers, most toddlers would happily wander into the road, why? Because they have no fear, no understanding it's dangerous. Many toddlers would probably be quite happy to pet a dog, because it's soft and fluffy and they wouldn't understand that it's also got sharp pointy teeth which could seriously injure them. Parents will teach their youngsters to only stroke a dog if it's safe to do so. Now supposing dad was walking with his toddler, dad was bitten by a dog when he was four and has ever since had a fear of dogs, he's very likely to pass that fear on to his toddler, not intentionally, but he's likely to react in a negative way, and his toddler will very likely pick up on that, because we're born with loads mirror neurones , which gradually die off as we grow up, but they exist to help us learn. So we copy responses from others particularly our caregivers. We learn fear as we grow, develop and mature, this is natural, this is survival at its most basic, the problem arises when the fear becomes greater than the threat and starts to cause physiological and psychological issues.
Again it's not just a learned response. For example an over active thyroid can cause anxiety. This isn't irrational it's due to an out of whack endocrine system. Some neuro divergent disorders can also cause anxiety it's not irrational it's different wiring in the brain, which we don't really understand. Peri menopause and the menopause can flick a switch which can cause anxiety, again it's those pesky hormones, which we still don't fully understand.
Brain tumours, Parkinson's disease, stroke, and pretty much most neurological disease can cause mild, moderate or severe anxiety. So to say it's irrational is too basic, yes it can be, but in many cases there is an underlying reason that might be psychological through trauma or physiological through disease or neuro divergence.