Without modern mobilization techniques, communication lanes and road networks, I'd find a relatively homogeneous city-state, alongside its nearby countryside population, to be more reactive and able to fully utilize its resources, as opposed to a far-flung heterogeneous empire which would need to assemble its distant subjects in another part of their empire and empire materialize them on the opposite part.
While I'm not aware of any powerful nomadic confederations poised to assault the Achaemenids in the East and capable of capturing cities such as Baktra, we do know of various nomadic tribes launching raids in the Upper Satrapies, and perfectly capable looting villages and small towns. In addition to those external threats, up until 19th Century, hill-dwelling tribes would sometimes descend to the valleys to loot and pillage across many parts of Afro-Eurasia, and the Achamenid Empire was full of such tribes.
For instance I suggest reading about one such tribe, the Uxians, whom Alexander fought, not on the behalf of the Achaemenids, but because they tried to extort Alexander in a similar manner they did the Persians, despite living deep in nominal Achaemenid territory.
Most of the Achaemenid subjects were neither Iranian nor Zoroastrian and those who were and were in high positions weren't all selfless and loyal people, Mazaeus, a Persian, simply allowed Alexander to take heavily fortified city of Babylon, while Bessus did what he did. Various tribal kings living in difficultly accessible areas weren't impressed enough with Achaemenid power to even pay them taxes, sometimes they preferred to actually tax them. And by taxing I mean robbing.
Speaking of Darius' regard or understanding of Alexander's true intentions, I think it would be good to mention that he didn't lend much support to his Satraps in Anatolia, and in relation to that how numbers Alexander faced began to increase after he'd already conquer most of Anatolia.
Mustering a Million men, if its true, is a quite an achievement, one that even the great Roman Empire didn't manage.
Which is why it's interesting to compare the numbers, as well as few other factors, between the Roman and Achaemenid Empires.
- Roman Army at its peak had 450K troops, according to Cassius Dio in the Battle of Lugdunum in 197, 300K were deployed, modern estimates range from 110K to 150K. This battle was a part of a civil war between Severus and Albinus and thus all the troops were Roman.
-Size of Achaemenid Army at its peak is unknown, however according to Herodotus they were capable deploying up to 2.65M during the Second Invasion of Greece, modern estimates range from 200K to 500K. we don't know if Persian had mobilized all of their available troops for this endeavor, however I personally suspect they haven't left their satrapies under-garrisoned and in my opinion they would have to do so in order to muster such massive numbers. In addition to that it took them several years to bring troops to Sardis and from there continue towards Greece.
After glorious days of Darius I and Xerxes I, the Achaemenid troops seems to have dwindled to "mere" 1M according to ancient sources, still better than the pathetic Romans with "puny" 450K and this is a relatively certain number.
When discussing the plausibility of numbers, one needs to talk of population.
The Roman Empire usually had 50-60 Million people, under Trajan around 70M Million, Achaemenid Empire 17-35 Million people. From this every 4th is an adult male. I can't stress enough that I'm being quite generous here because until the 19th Century couples usually had more than two children.
Romans had 450K troops out of, 50M, I'll use the lower estimate here which brings us to 12.5M adult males, that means that nearly every 28th adult male was a soldier, if we take that the Achaemenids had 1M troops out of, I'll use the highest population estimate of 35M which brings us to 8.75M adult males, that means that nearly every 9th adult male was a soldier.
Even when skewing the numbers in favor of the Achaemenids, by several factors, such as population number and breakdown, deployment - 1M were at a single battle, while Roman 450K never were, which would mean that the Achaemenids would need to extract an even greater number than 1M because, as I've said previously, someone needs to man the garrisons, such ability to mobilize every 9th male not withstanding serious economic and political consequences, would require a tremendous logistical and organizational effort and their deployment would be severely hampered by the state of Achaemenid geographic constraints.
Now onto actual battles.
Until Granicus in 334 it appears that Darius didn't consider Alexander as a massive threat that would require the maximum mobilization of his troops which can be seen from the fact that Alexander's numbers at Granicus were merely matched, a single year later 600K troops are at Issus and 2 years after 400K more. In short, by ancient sources at Granicus Alexander faces 40K, at Issus 600K, at Gaugamela 1M, by modern estimates it's Granicus 40K, Issus 108K, Gaugamela 120K.
Maybe modern estimates are two low and losing battles when having 2.7:1 and 2.5:1 advantage against a not just superior, but brilliant tactician, isn't that much of failure when you're a decent commander, however losing when having 15:1 and 21:1 advantage is beyond spectacular failure, even if one's an inferior commander. If we halve the numbers and get 7.5:1 and 10.6:1 advantage the failure is still spectacular.
Why did Darius even fight at Gaugamela when seeing how bad he was at Issus, when defeated at Gaugamela why did he even flee eastwards, at that time the Iranian Plateau was still far less populated and poorer than Mesopotamia and he lost a 1M troops, it's highly unlikely he'd be able to find another 1M, and let's face it how bad he is he'd need at least 2M, to get that decent 42:1 advantage.
It all boils down to whether or not Alexander's victories were impressive enough unless he was outnumbered at least 4:1, personally I'd say yes. If the numbers are true, Darius was either mentally impaired, or it was true what so many ancients believed, Alexander was divine. Lastly, ther's something special about the Achaemenids because no other state deployed such numbers on the battlefield apart from the Chinese during the Warring States, if we are to believe their ancient sources, and If I'm not mistaken, even they didn't have a 1M on the battlefield.