1. 5e hp is defined as a mix of various things. Removing all but 1 ingredient from that mixture creates a new mixture that is not the same mixture as the other mixture. I tried to say this when I started talking about abstract hp but did a poor job of adequately and correctly explaining my thoughts.
All but one ingredient need not be removed for the majority of damage in the game to be represented by one of the ingredients while others are then used when most necessary. The argument that was often used to address the point i brought up about injury poison only being able to be delivered if by injury was argued that in the instance of injury poison an injury could be made while in the instance of other attacks and instances of damage being done injury was not demanded for and thus could be substituted for one of the other 3 ingredients in what damage actually is.
I have reformed my position some what from being a purely physical durability as hitpoints interpreter to one that simply uses physical durability as default until otherwise specified by the rules of the game. My reasoning behind this will be explained in my response to 2.
2. Damage types have no mechanical impact unless a mechanic like vulnerability is invoked. The importance of that point has always been that damage types do nothing on their own. Instead it's the vulnerability mechanic that causes a monster to take additional hp damage and not the damage type mechanic at all. As such your claim shouldn't have been about the existence of damage types, but instead the existence of vulnerabilities. .
The mechanical impact of damage types is dependent on immunity, resistance, and vulnerability. simply because they arnt the same concept doesn't mean they are not related to each other. Immunity, resistance, and vulnerability are related concepts to both hitpoints and damage, and as abstractions the related concepts to hitpoints and damage have a baring on how those concepts are defined through their subordinate concepts. If these related concepts could contradict the abstracts of hitpoints and damage then the connection between them as concepts would be dissonant, one concept would be disagreeing with the rules of another concept. So immunity, resistance, and vulnerability give further context to the meaning behind damage types meaning they also inform the meaning to hitpoints because of their association. Now you can certainly argue that whatever meaning to hitpoints though immunity, resistance, and vulnerability that damage types give hitpoints is dependent on interpretation of each, and i can concede that point, as others have made that point before and i never argued it to be illogical, but this means that what damage types are has baring on what hitpoints is at least incidentally. Concepts may be abstractions, but the connection between concepts is always concrete whenever the connection must be formed.
All that's happening with your argument is that you are assuming that the vulnerability condition's only explanation is due to meat, but when put in the context of vulnerability, it's trivial to see that all the vulnerability mechanic does is make you lose additional hp when a criteria is met and since hp is defined as a mixture of more than meat in the rules then there's no implication based on the vulnerability mechanic that the damage being inflicted needs to be meat damage
With each damage type a question must be made as to what relationship there is between what the game states this damage type represent and the vulnerability (resistance and immunity) the target of the damage could represent. The vulnerability is the responsibility of the concept of hitpoints to explain, via the 4 concepts of hitpoints, physical durability, mental durability, will to live, and luck. because there are 3 concepts being described that also creates 3 different facets of the damage-type/hitpoint relationship. That leaves a lot of room for interpretation, and the game gives gm full opportunity to interpret this any way they can. most of my arguments fall upon what a gm CAN interpret damage types through the concepts of immunity, resistance, and vulnerability and whether or not that should have any baring on what hitpoints actually means when those concepts dont happen to be present. What a gm CAN interpret hitpoint lose as in this situation is ultimately a compromise between the rules and their imagination however i hypothesis due to what the damage types mean within the context of immunity, resistance, and vulnerability will tend toward physical more often than not, and also that tending toward physical when other options are available will still be the option that is preferred by most peoples interpretation of the rules simply because of the meta we bring to the table.
further thoughts
Ultimately my argument has changed slightly from one of ignorance to the possibility that other concepts of hitpoints are meaningful in any way to combat narratives in D&D 5e (and probably other editions). But i have shifted to an interpretation where i significantly favor one subordinate concept of hitpoints as a default over others until a mechanic of the game presents itself to be clearly connected to a different subordinate concept of hitpoints, in which case it takes president. I dont just how this opinion out of personal preference alone though, it is backed up by my statement about how the mechanics of D&D actually work and my analysis of them. Those statements and analysis are open to valid criticism but what i expect of valid criticism is to consider how the rebuttals ive made to other criticism of those statements relate the validity of future criticism and if they back up what ive said or not. Do not just value my initial statements by themselves but also in the context of being reinforced by arguments that defuse criticisms that have been raised to them, they are of equal value.