As the rules are currently, there is simply no way to emulate any injury other than a relatively minor scratch that is good to go after a single night of sleeping, without a fairly major house rule (major in its variations from the norm as represented by the rules).
This is pure and simply a
fact, therefore there is no interpretation of HP that can change this. The current rules, no matter the verbal description, simply don't support lingering wounds from physical combat (although there are lingering effects from spells and special effects, but this is not the point here).
It's a pity, because this clearly invalidates one gaming playstyle. I do not necessarily prefer such playstyle over others, but I wish D&D would support as many playstyles as possible. With regards to lingering wounds, I can at least identify a minimum of 3 playstyles:
- continuous play: HP (and possibly other resources) completely refresh after each encounter
- fixed-window play: HP (and possibly other resources) completely refresh at a specific time, normally 1/day
- moving-window play: HP (and possibly other resources) gradually refresh at a specific time or after an interval (normally complete replenishment takes >1/day)
They're just different playstyles, so it's pointless to argue why one's favourite is better than another's, because it isn't.
If published adventures are written assuming the party is at max hitpoints every day, that will drastically change things for parties using a house rule to alter this.
This is probably what makes it so difficult to support all the above...
Dialling the time window lengths or equivalently the amount of HP regained (or changing the details of what is a "short" or "long" rest), making other variations (e.g. switching between fixed amount regained vs rolling dice) are easy house rules, but unfortunately
published adventures are going to assume everybody uses the default.
At this point, the best they can do is probably include a chapter in the DMG "Adventures design" with guidelines about how to change a printed adventure when switching between these playstyles. Unfortunately IMHO it's always easier to increase the power (ie faster healing > more encounters!) than decrease it (slower healing... ehm... less monsters? only to some extent really).
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Another issue is wanting to include a
wound system, by which I mean a system with actual
temporary penalties replacing HP damage for representing physical lingering wounds.
That is actually quite different, and even more complicated to handle in adventures design.