A lot of it comes from the fact that some of the original mm1 minions are poorly designed. They either don't do enough damage, have no special ability that makes them a pain, or have no special effects, and are melee creatures.
The crux of the issue is this, the marginal benefit of attacking minions is such that they are always most valuable to attack first. BUT the marginal benefit to the DM is not so clear. Since the rest of your normal monsters are unlikely to get another encounter attack off, the "1 hit" buffer the minion adds for single target attacks is just a portion of the damage a standard monster typically does. This means that the 4 minions are almost always worse off than just another monster which also provides that same buffer[assuming it goes down in 4 hits, if it takes more, it has a larger buffer], but also adds some sort of encounter ability.
This means that the original MM minions by an "opportunity cost to players" they look like they should be good under the assumption "attack the biggest threat". Since players take them out first they're the biggest threat. But the truth is that the opportunity cost to the monsters in the damage that monsters deal out is a lot more important. Such the original MM minions are designed much weaker than they ought to be.
Such, to make minions be a threat you need to exploit some things
1. Special abilities
2. extra damage
3, bonus on death
4. range.
IMO ranges is the biggest one. Look at for instance a situation with 4 regular monsters and 1 minion group. If the minion group is in melee then everyone gets to take the most optimal option of attacking the minion group and they do so at little to no penatly. But if the minion group is hucking javalins then the melee players must sacrifice their body via OA, or their ranged allies[by letting enemy melee past them] in order to get the damage on the minions, which is the most optimal option to reduce incoming DPR. The range also allows the minions to spread out making it harder for wizards and sorcerers to use their AoE abilities to the fullest.
This does two things, it prolongs the lives of the melee enemies because the ranged strikers and controllers which would otherwise be laying down status effects on them are no longer able to. And it prolongs the lives of the minions since they receive less attacks per round. On the whole, the enemy group is going to go down in roughly the same number of attacks/rounds, but they're going to get more actions out of those rounds and/or be able to hit the softer targets easier(more bang for their buck).
If those minions were melee minions none of that would happen, since the melee players would not suffer any penalty to hack the melee minions down and any round a melee minion spends not attacking and getting position is an attack it is wasting