Hello, thanks for contacting Healthcare Magic. On the point of your problem, first of all, i would first or all like to call your attention to your loose tooth... As you imply, your tooth is quite loose (mobile), that itself implies that the supporting structures to the tooth have become eroded, and hence probably cannot be saved (your dentist
can explain better), also, you reported of experiencing pain in the same tooth, which implies inflammation (probably due to infection) in the periodontium
of the tooth. The infective inflammatory infiltrate destroys the periodontium, and if more than half of the supporting structures of the root of the tooth are destroyed, then it is always better to extract the tooth, than try to save it (the status of the periodontium will be clear on an IOPA X-ray).
Now, addressing your query about an implant, yes it may be the best option, if your alveolar bone is strong enough, if your blood reports show adequate levels of Calcium and Phosphate compounds, and if you are not allergic to the bone graft material (which usually people are not). But, it may not cover the gap (also known as a "mid-line diastema").
Now, comming to the "capping", in-case your adjacent (unaffected/normal) tooth is rotated, or mal-aligned in any way, then trying to cap it may be disastrous, as the "bridge" (or the "multi-toothed" cap) may not remain stable, and can anyway then result in a periodontal disease of the healthy tooth itself, and then it will need to be extracted anyway.
All in all, you do have valid objections, but you need to clarify them with your treating dentist, as he/she is better versed
with your condition.
Hope that this is helpful to you.