Should I replace the top four front teeth with a dental plate? (photo)

Aesthetically, you can always reach an option with a plate or a bridge. However, I think another good option for you could be extractions and dental implants. That way it is better to have a very strong platform, that its going to receive all the pressure of your bite. You are young, so your bone density should be fine to hold regular dental implants.

Implants ARE the
permanent solution! However, you may need some time for the bone to heal before
immediately placing the implants into your mouth. You would also want a
prosthesis to fill in the open space while implants are healing, before they
can support a bridge. A temporary flipper or upper partial both sound like a
good temporary solution until your mouth is healthy enough and disease free to
support implant placement. Be sure to stick to a strict hygiene regimen and
regular cleanings to prevent the disease from spreading to your other teeth.

Implants could be one good option in your situation as you described it. You can ask your dentist about possible immediate loaded implant to take care of esthetics immediately.  Otherwise you can get extraction with bone grafting to get ready for implants in future and wear your plate during healing period.  Best of luck