Does a post and core seem like a good idea for the crown on this tooth?

[Concernedpatientyo]

I would like to hear more opinions on this matter. Had a pretty bad infection that was dormant for 2 years post a dental filling. RCT was denied at the time. A cyst sort of popped out on the side; below the tooth in question. An RCT was done and canals were cleaned out. Was told that new caries were found around the top surface and sides (as shown by the white filling material). I was instructed to get a post and a core done as part of my crown procedure (not covered by insurance). Wanted to see what you guys think about that? think the tooth needs a post and a core? would it help the tooth? or is there not enough information available from the images I uploaded? I was reading how the core and post is only necessary when no visible part of the tooth remains, but googlefu seems to be failing me.

 

[Dr M]

I would need to see an x-ray to determine the amount of healthy tooth structure that is left.