I think you see a problem based on a misunderstanding - I dont think RPGs are about modelling reality. You have focussed on endurance, but in a similar way, it doesnt make sense that an untrained person gets a -25, then suddenly jumps to a +5 in every use of a skill once they get one rank. In the real world you get a bit good at the easy things, but a raw beginner at something is no better than a totally unskilled person when trying to do the extreme things.
An example because I'm in the mood - I'm a juggler, I can juggle 9 balls for a couple of seconds and then stop. I guarantee you that if I give you 1 rank in juggling (ie teach you to do 3 balls for a minute, say) you will be no better at replicating my 9 ball effort than someone who has never picked up a juggling ball - modelling this is just too much effort, most of us want our heroes to have some slim chance of pulling off the incredible and gradually getting more and more superhuman. If you remove endurance, do you also reduce the rate at which people get better at skills? That is also unrealistic within almost all RPGs (it's particularly apparent with learning languages imo, but if there's anything that you are really, really good at - consider how any game would replicate that skill and I'm willing to bet you'll find it lacking)
Ultimately, the rules arent a model of reality - they are a mechanic to produce fun. The ultimate result is that experienced heroes pretty rapidly become "better" than beginning heroes. That's the limit of it. Heroes in fiction can fight through hordes of minor enemy cannon fodder, ending up covered in blood, with arrows sticking out of them, fighting on through sheer grit and "heroness". That's not realistic - a few semi-skilled armed people will overpower all but the most skilled fighter, but it's not meant to be - when you played cops and robbers as a kid, how much time did the cops spend filling in forms and obtaining warrants?
All something of an aside. The beauty with HARP is that it is eminently customisable. If this particular unreality bothers you - just forbid endurance from being developed and your problem disappears (though the result will be that a weak beginning character will have no chance of surviving at the higher levels imo)