After two years of treatment, it sounds like you are almost done with your orthodontic treatment! Elastics/rubber bands are used throughout treatment at various stages for differing purposes. Towards the end of treatment elastics help to finish the bite so that the treatment result is stable. For example, if the top and bottom front teeth are touching a little too hard when you bite down compared with the back teeth, after treatment the upper front teeth may start to space out and move forward from the excess pressure. Wearing elastics from the lower front teeth to upper back teeth applies pressure to slightly move the lower teeth back. This fine tunes the bite so that the front teeth do not have an interference when you chew that may cause unusual wear or spacing. The way that you have been wearing elastics throughout treatment commonly changes in the final few finishing appointments.
I agree with your orthodontist. 14 months is a relatively small investment in order to have a lifetime with a natural, healthy tooth in your mouth. Also, implants are not maintenance free and there is quite a bit of surgery and dental work that would need to be done in order to restore that tooth. There are risks with surgery such as infection and occasionally there are implant failures when the implant does not integrate with the bone. In my practice 40% of my patients are ages 18 and older. More and more adults are getting braces, you will not be alone!
It would be best to call your orthodontist and let them know what has happened because:1) Without a bracket on the tooth, that tooth is not moving! It may slow down your treatment2) Although the wire is not bothering you now, it may bother you over the weekend and it may not be possible to be seen right away3) Your regular adjustment visit is usually scheduled for a short appointment in order to adjust the wires. Replacing a broken bracket takes more time. It would be courteous to let them know so that they can plan enough time in the schedule to repair a broken bracket for you.
It's very common for orthodontists to place upper braces first and wait several months before placing lower braces. Some reasons may be:1) Because of the way the upper and lower teeth fit together, the upper teeth may need to be moved out of the way first before there is room to place lower braces. Otherwise you may bite on the lower braces and either cause damage to your upper teeth or break off the lower braces.2) There is more work to be done to the upper teeth and since patients prefer to have upper and lower braces removed at the same time at the end of treatment, your orthodontist may be getting a head start with the upper teeth without needed to place lower braces yet3) I often give patients a chance to get used to the upper braces in regards to soreness and learning to maintain the braces before jumping into a full mouth of braces. Think about how much harder it would be to eat if both your upper and lower teeth were very sensitive at the same time!