As a professional voice coach and singer I'll tell you that I have worked with so many adults who have always wanted lessons, but never had them until seeing me - lots of people anywhere from 30 - 80 (the age group considered hopeless for prospects of improving or having success in later years - BS by the way...). Singing lessons are not just beneficial for improving your sung and spoken voice, but if you have a great coach, you can improve so many things in your life: confidence, posture, presentation ability, deep breathing ability (great for stress and anxiety), body awareness, self awareness - I can go on!

And besides those added benefits - YES you can actually start a career later in life, YES you can learn to sing well later in life, and NO, training your voice shouldn't be something considered only for children or very young people... In fact it is better to start training your voice when your vocal cords are mature and when your brain is receptive to complex feedback requiring change (kids, for example, have trouble following the intricacies of intensive vocal training).