I am currently reporting old (pre-1.16) plants not being able to be potted as this inability may be an oversight. There is a reasonable likelihood these tickets may be considered feature requests, however the fixing of MC-170833 and MC-214684 as well as the non-Invalid Works as Intended resolution of MC-182822 make this seem less likely. As many of these have remained non-pottable for up to eight and a half years, this ticket may instead be considered Works as Intended if they are not planned to be made pottable like newer plants have been (the changes made to pot handling in 1.13 may have changed the viewpoint on this and its doability). With the above information in mind, this will be left up to the mods and/or Mojang to decide.
Despite many other plants being able to be placed inside of flower pots, these cannot be. It is not known if they are intended to not be placeable inside of pots, or if this is an oversight.
Affected plants:
minecraft:wheat
minecraft:carrots
minecraft:potatoes
minecraft:beetroots
minecraft:melon_stem
minecraft:pumpkin_stem
minecraft:nether_wart
minecraft:cocoa
This is a feature request.