Consequences of Not Addressing Extracted Teeth?

Your question has a lot of different factors that can affect the answer. Firstly, it depends on the condition of the rest of your mouth, how many other teeth are missing and their condition and position. The best thing you will want to do is consult with a dentist and do a comprehensive evaluation to evaluate exactly those factors. You will want to restore the missing teeth whether its with implants, bridges, or a partial denture so that your other teeth don't shift. Once the teeth shift around, it can require braces to move them back if you want to get implants or something else to fill spaces. Also, once teeth are missing, especially when it's multiple teeth, that puts extra stress on the remaining teeth to make up for what's missing. This extra stress and force can wear or even breakdown the remaining teeth causing problems for them. Hope this helps!

Not restoring missing teeth may lead to several issue down the road.  If you leave your right side with out upper teeth, you will be force to chew on the left side.  This will cause excessive wear on the left and possibly tooth loss on the left.  If you don't want implants, you only alternative is a partial denture.  It may not be the best thing, but it's better than doing nothing at all.

The most obvious and detrimental consequence of not replacing a missing tooth is bone loss. When the teeth are present and in function the bone is maintained .Simiiar to an aging adult that avoids serious osteoporosis through resistance excercise. By not replacing a tooth post extraction the ability to provide a successful denture, bridge , or Implant  is compromised due to a loss of bone.

Dental implants not only aid in the retention of dentures or crowns, but they also promote the maintenance of bone. Placing a Dental Implant after an extraction has numerous benefits. Among them is stimulating the bone so that a defect will not occur.

Even if teeth are not visible, such as is in your case, they should be replaced after being extracted otherwise certain consequences may occur.  Immediately after teeth are extracted, bone begins to resorb or shrink unless the teeth are replaced immediately. The opposing teeth will continue to drift or move until there is an equal and opposing force.  They might even drift and touch the opposing gums where the extracted teeth once were.  Since a large portion of one side will be without teeth contacting, your bite will change possible causing muscle soreness and tension leading to TMD (TemporoMandibular Joint Dysfunction).  This will eventually occur because you will tend to naturally favor the only side that has teeth.  Once this process of drifting and shifting of teeth occur, your front teeth will inevitably have to much stress to bear and will tend to splay or drift forward.  Though I am presenting the worse case scenario, any of the above mentioned consequences can be corrected with replacement teeth.  Your options would be a removable denture or a fixed bridge supported by implants.  In my opinion, your best option would be the implant supported bridge.

Implants have better longterm success than partial dentures which can be option for you. Facial sagging with limited chewing and esthetics are concerns with no replacement. Adjacent and opposing teeth with shift and can lead to problems which in result in loss of more teeth in quicket time. I will definitely recommend replacement.