Block Entities are not properly removed when 64 or more blocks are changed at the same time in a single chunk

The bug

This is a rendering bug to do with Tile Entities in a chunk. I have provided screenshots which aim to show how to reproduce too.

If you have 64 or more Tile Entities within the same chunk and then "delete" them, using either /fill, /clone or (if they are signs) retracting them using pistons, when you place a new Tile Entity in that same spot, the previous Tile Entity will render over that or instead of the new Tile Entity.

For example, if you have a wall of 64 chests, do /fill to get rid of them and then place a beacon down where one chest was, you'll get a chest that's rendered inside a beacon. If you place a sign down you get an error that says "Unable to locate sign".

All rendering errors and effects are cleared with a relog, so perhaps this has something to do with the way chunks are updated or saved?

How to reproduce

1. Press F3+G to make sure the blocks you are filling are in the same chunk
2. Use for example the /fill command to place 64 or more tile entities

   /fill ~1 ~ ~ ~5 ~4 ~4 enchanting_table
   

3. Use for example the /fill command again to replace these tile entities with different tile entities

   /fill ~1 ~ ~ ~5 ~4 ~4 ender_chest
   

Code analysis

Code analysis by Marcono1234 can be found in this comment.