In a 2-player game the rounds are over quickly so the sword is a worthwhile investment I think, that is even if I'm hurt while beating a monster I will be recovered pretty quickly to harvest the fruits of my battle. Since recovery is fairly quick the rewards for the monsters are also more valuable, there will be a total of two-three actions until I'm able to utilize whatever workers I have left and four-six actions until I'm fully recovered.
What this means to me is that I can almost be certain that whatever cards I may or may not know be under the monster aren't all taken, and that I haven't sacrificed myself just to let my opponents dig freely. Despite being a 2/3 chance of hitting I've often seen all or almost all of my adventurers go while defeating a 2hp monster for 2-or-so XP and not enough gold to pay for the sword investment (and certainly not the hospital costs).
The issue is that in a three or four player game, it's not two-three and four-six actions until I can start digging again but a lot of them while I paid the same price for the sword and got same rewards for my kills. Wouldn't a small price reduction for games with many players make this wager more fair? In the printed board game this could've taken the form of another side on the board where either the sword was cheaper (perhaps 2 instead of 3 gold) or where hospital costs were lower (probably not a good idea as it'd put the take-XP-and-go-to-the-hospital cards out of balance).