The earlier editions also had this interesting thing where everyone rolled their hitpoints, even monsters. Combined with that was the fact that everyone's hitpoints were so much lower.
That meant that a significant proportion of monsters were effectively minions, but cost full encounter budget (not that there was such a thing). Just think how often the wizard pulled out fireball and an encounter was either outright ended or reduced to 1 or 2 monsters who took a single hit to dispatch.
I think it would be possible to play 4e in a 1-2e style, simply by swapping out 2/3rds of monsters for minions and then not making it up in the encounter budget (but still award the correct minion xp - to simulate that slow levelling curve). You would also not tell the players which creatures were minions in this case.
I would probably also implement some sort of "much bigger crits for monsters" rule, say 2d8 per tier? Again trying to simulate that "sure this encounter is a pushover, but someone might still die if we're unlucky" factor that old editions had.