I kinda agree with a lot of folks here, even though waking up with high or low health does give you a special message, a few finer health monitoring items may be pretty cool, give you more reason to loot hospitals. Because honestly once I have a couple antibiotics and some basic painkillers I find little to no reason to clear out a hospital.
Could even be in tiers:
a basic health watch that gives you a general idea of your health kinda like what you get when you wake up now, but viewable anytime while you have it handy. Maybe a bit finer than the wakeup messages, but not by much.
A bit of a kick to that is that it takes wounds into account, giving you a lower health reading than you actually have if you have a few wounds for example, being more of an athletic fitness watch more than an actual medical tool. Such things could be found rarely on zombies, or in houses, kinda like an alternative to a game watch.
Next would be some kind of portable medical scanner. Think like a star trek medical tricorder but more low tech. Designed to streamline medical exams in the near future. Takes a small blood sample (+1 pain on use) and then gives detailed information based on first aid skill. At 0 skill it only tells you if you have a cold, flu, fungal or parasite infection, and always says there is an 'unknown blood contaminant'. Making the watch more useful to the untrained. But at 1-3 skill it works similar to the watch, giving the character enough information for a general health assessment, unmodified by wounds. and at 4 first aid and above it gives you the actual numerical value for your current health. Such tools would only be found in doctors offices, and hospitals. Maybe rarely in labs and ambulances.
Finally would be a medical diagnosis system. A somewhat bulky computer with testing equipment built in. Completely unusable for anyone with 0 skill. Works similarly to the portable medical scanner at first aid 1-3, maybe with finer detail. But at 4 and above it gives you all the information you need to know about your health, current health level, as well as your current baseline health. At even higher levels it could even treat minor illnesses like the cold or flu. Not removing them entirely, but acting like cough medicine at the cost of some extra battery power. Such things would only be found in hospitals, and the more technical lab finales. And while small enough to be man portable, it would be large enough to be impractical to lug around everywhere.
...ok that got bigger than I expected. tl;dr I feel items to give us finer health details would be welcome, and may even give us more reason to check out hospitals, which currently only seem mildly useful in niche situations, like yer a computer whiz with a broken arm and for some reason can't make a splint.