Except as pointed out, they don't have sufficient presence unless you're talking about divinations, scrying and teleporting at will. The specialist adventurers would crush the bandits they can find like a grape, but are ineffective for the reason that all the other bandits are going uncrushed.
20 Warrior 3s with bows would dismantle bandit groups, which tend to be half that number and about the same level or lower(considering someone higher level who can't find a better paying trade being somewhat unlikely unless the country's average level is somewhat higher), would slaughter them effectively.
And for orcs, again, the 20-40 orc raids would be dealing against their number of infantry in basic fortified positions, where the advantages of reach and massed missile fire(while having cover against return fire) against traditionally lightly armored raiders would put them down with lower losses.
Both of these are regenerating threats. More bandits will show up as long as you can't keep detection high.
A possible sequence of events:
Groups of 10x Warrior 3 Bandits infest a dozen routes scattered around the country. Adventurers presumably are based in the capital. Militia are presumably patrolling lightly, so lets say a 2-3 day cycle is in order.
PC-route:
PCs spend a divination(costing XP or gold) to learn about the most urgent bandits location OR wait for the days it'd take for people to realize merchants are disappearing along a particular route and submit a Request For Adventurers. The former would cost extra, given that you're spending good XP to find out out low-CR bandits to defeat, which won't get you much XP back.
PCs spend a teleport to arrive in the right area. They take a couple of hours to get their bearings(unless using a higher level teleport, they'd be likely fairly off target most of the time) and track the traces back to the bandit lair or they spring an ambush thats expecting merchants.
Ambush is defeated in a round or so, as a fireball wipe out half the bandits at one go. Two fireballs or melee wading in later, the bandits are gone. The XP gains are rather low, risk is low(at worst they might have scored some 10% health loss on one or two unlucky guys with an arrow), loot isn't even worth collecting with the non-masterwork leather armor and weapons, though I suppose their resale value might pay for a divination's material component.
Adventurers teleport home or to the next bandit site. Assuming they prepared 3 teleports and know of all the groups ahead of time(possibly with some particularly inspired use of divinations), they dealt with 2 bandit groups in one day(taking a few hours each), and spent the last one teleporting home.
They take a total of 6-13 days to clean out these groups of bandits, assuming they used divinations at least weekly to detect for threats. Divination is fairly inefficient, since it can't answer general questions(you'd need a lot of castings to identify province and route), Commune is better but costs that 100xp..
Militia route:
Presuming 15-20 men per militia patrol, the patrol routes would probably take between 3-6 days to complete, at some point along the route, the patrols would run across the bandits in their area.
They then move to engage said bandits(since they are already there). With a 2:1 numbers advantage, they'd likely kill half the bandits outright in the opening round, with a small but present risk of the bandits wounding or killing 2-3 men in the process.
They mop up, retrieve their dead and possibly scoop the bandit gear up.
They'd have mopped up the bandits within 3-6 days including detection, and lost a number of men. New ones would need to be hired, but fortunately all the gear is still there so the cost is lower. As long as patrols are kept up, new bandit groups would be difficult to form.
So to say that a mundane army can't deal with mundane threats is false. Thats exactly what mooks and fortifications are for, to deal with all the trivial stuff so the heavies can spend their efforts more constructively. The pay scales are completely out of whack, since hiring the militia is lower costing for better coverage.
To use level 10 adventurers for this is using racecars in a traffic jam.
