In the immediate future, bleeding will still stop immediately when treated, whether you bandage, cauterize, or just hold a rag over it (though rags have a chance of not working). That’s seperate from healing over time that’s being proposed.
It’s possible that in the (far) future there could be some kind of severe bleeding wound that you can treat partially, say by slapping a bandage or something over it, then have to do something more involved to make it stop fully.
As for the system encouraging “moping around the base”, this is a symptom of HP systems in my opinion. If you give someone a single score representing “not dying”, especially if it has very coarse numbers*, they’re going to tend to try and get back to “full health” as a priority. Roguelikes are very guilty of this with a combination of high danger and ample options for healing. In reality, do you sit at home and rest every time you have a cut, scratch, or bruise? How about if you have a broken leg? Do you just shut down until it’s all better? No, you generally tough it out unless it’s so bad you can’t function (after treating it as appropriate). Over time your wounds heal, and meanwhile you get new ones, it just happens, people walk around getting on with their lives with minor and sometimes major injuries all the time. That’s what this system would mean, you’d get bruises, cuts, scrapes, burns, even bites and maybe broken bones, but you treat them and keep going, because the alternative is dying. That’s survival.
*Just 100 HP is pretty damn coarse, imagine the smallest wound that might register as a wound, a cut, or a scrape, bruise, a small burn, or stubbing your toe. Now imagine 100 of them, is that going to kill you? No, meaning 100 HP is too coarse