Is a bone graft and implant necessary after extracting tooth #15?

The decision to replace a back tooth or not resides with you but the doctor's recommendation is based on his assessment of your chewing function, occlusion, and other factors. To avoid excessive pressure and wear on opposing sides of the missing teeth, you'd want to preserve balance. Whatever you decide, a bone graft is highly recommended at the site of extraction to preserve the ridge there and avoid excessive bone loss.

If you wish to regain the ability to chew again on this tooth then yes you would benefit from bone grafting and an implant. If the goal is to not get the tooth back in this position then you would not require it. One of the risks of not getting a tooth there can be that your opposing tooth on the bottom can rise up into this space over time (happens in some individuals over time),