Depends on your health insurance, financial standing and free time. If you're an affluent tech worker you probably would go to a dentist for a toothache. Most people I know would not.
I wouldn't compare mental health to broken bones. We've been successfully treating broken bones for thousands of years. Seeking treatment for depression or generalized anxiety is more similar to seeing a doctor for some poorly understood malady like ME/CFS or IBS. No one really understands what's going on or why. You might try some medication or treatment and it might work, do nothing or make things worse.
It's worth a try but it's not a silver bullet. If your life sucks and your future prospects are bad then therapy is really just helping you cope.