Do I need RCT on tooth #30 that has external resorption or should I extract it and have an implant? (Photos)

I have had many teeth like this over the years that have been saved long term.  It is important to understand that many is not the same as ALL,
Once the necessary root canal treatment is completed and the area debrided the external/ internal resorption should stop.  In my experience most external resorptions are actually a combination on internal and external processes.
It is very important that great care is taken in placing excellently bonded post and core restorations to create a solid foundation for a future crown.
Tri-Minerl Aggregate can be used to seal perforation and promote healing.  I would probably wait before placing crown to make sure treatment was successful.
Extracting teeth does kill thousands of brain cells primarily conneted to the PDL of the tooth.  

While we all hope for the best, there are some situations that simply may not be work the effort and cost.  I have yet to see an external resorption case successfully treated by anything OTHER than extraction.  All the other treatments are simply delaying the inevitable. 

Unfortunately, I see no way to save this tooth. It appears by the time you go through a root canal and gum surgery to allow crowning the tooth and spend the dollars on trying valiantly to save the tooth, you could place an implant and crown at less than the total cost of trying to save the tooth. You will get more value with an implant and crown. Hope this helps.