Step forwards
Many of us have learned to plan our lives better and not be as dependent on a watch.
If you check the time so often that the few seconds it takes to take the phone from your pocket is inconvenient, you aren't managing your time. Unless you are taking medication that must be precisely timed, you should easily be able to manage your schedule. A person makes a victim of themselves if they ever find themselves unable to schedule. If you have to be somewhere at 10am, leave with enough time to get there at 9:45. If you're running late because of circumstances beyond your control, call and apologize and inform the person "I have encountered unforeseen difficulties. I will be a little late." Then next time, account for additional delays so they don't believe it is habitual.
If you're stressed over time because of conflicts of work and daycare for example, cut back your hours, change day cares, change jobs, hire an au pair, hire a teenager near the day care, make an arrangement with a parent to take turns picking up and dropping off with, etc...
If $500+ watch is in your budget, your life would be better if you spent the money to buy time instead.
Some people believe a successful person wears a fancy watch. Smart people know that success is learning to manage your life without one.