I dispute the assertion that 4e is automatically “heroic”, and that ability scores are as critical to having an effective game as is made out. 4e seems heroic because the default setting for creating encounters is set to “easy”. If you used the same playstyle to run a 1e game, the characters would seem just as heroic.

Also, ability scores seem essential only because the game tells you that players need to succeed in d20 rolls most of the time.

Take a first level, 1e fighter equipped with a longsword, scale armor and a shield, which is relatively typical equipment until you score some loot. His stats are rolled, so lets say he has a strength of somewhere between 10 and 15, and a constitution of between 10 and 14. He has an AC of 5, does 1d8 damage and on average will have hit points of 5.5.

Let’s say he is fighting a hobgoblin, which has an AC of 5, does 1d8 damage and on average will have hit points of 5.5. So in that respect they are essentially identical.

However, the 1st level fighter needs a 1 to hit the bugbear, so he will only hit the hobgoblin 30% of the time. The hobgoblin, by contrast, hits the fighter on a 13, or 40% of the time.

Using the standard random monster generation table, if the fighter is on the first level of a dungeon he could encounter 2-8 of these, so using the large parties of 1e (padded out with hired mercenaries and henchmen) that is not so bad. However, if he descends to the second level he would encounter 4-16 (and would get double the treasure). If he goes to the third level he would encounter 6-24, but if he defeated them he would get triple the loot.

And it is still possible on the first level of the dungeon to encounter, for example, 2-5 bugbears. Each bugbear has an AC of 5, an average of 14.5 hit points (ie. 164% more than the fighter), and hits the fighter on an 11, or 50% of the time, while the fighter still hits the bugbears only 30% of the time.
By contrast, in 4e a first level character is generally fighting monsters that are considerably weaker than him. A level 1 standard monster is nowhere near as tough as a level 1 PC. A level 1 elite is probably more of an even match.

The point buy system pretty much ensures that the lowest strength score a fighter is likely to have is a 16. A level 1 fighter with a 16 strength using a longsword is +7 to hit, and will hit a level 1 standard skirmisher (with an AC of 15) on a natural 8, or 65% of the time; he would hit a soldier 55% of the time. If you somehow contrived for that fighter to have a 10 strength (which I don’t think is even possible using point buy) he would still hit an at-level soldier 40% of the time, which is still much better than the 1e fighter fighting the hobgoblin.

The 4e game feels heroic because the publishers advance different expectations, but there is no reason why you have to buy into those expectations. A game with potentially low ability scores could be run if the party was willing to run away when necessary, pad out the party with henchmen and hirelings, accept a lower frequency of successful attacks, pick its battles, pay close attention to tactics, and choose lower risk fights.

Note this last requires the DM to adopt an approach where certain areas are, on average, predictably more dangerous than others. Lower levels of dungeons are more dangerous than higher levels, forests are more dangerous than roads, swamps are more dangerous than forests. Parties can then choose heir level of risk.

Another reason why 4e is no more “heroic” is that the good utility powers actually come later in the game than in other editions. Most characters don’t even gain access to non-combat utility powers until level 2, whereas spellcasters get them at level 1 in 1e (think feather fall or jump). And the next tier of spells, which in 1e you get at 3rd level, you don’t receive until level 6 in a 4e game (think levitate or invisibility). In terms of resources, a 1st level 4e party actually has less to work with than a 1st level 1e party.

So a zero to hero campaign is completely doable using 4e. You just can’t drink the kool-aid.