can't the Romans win by simply bringing lots and lots of missle troops to the playground? Horse archers can't defend well...
Personally I think that had Crassus brought lots of light troops and simply formed testudo and square formation then there isn't a lot the Parthians can do. And even if Crassus didn't know, Anthony sure would have. So why didn't the Romans do that?
Let's say Crassus forms up a square, but he's had the foresight to bring loads of auxiliaries equipped with bows and slings and whatnot.
Could the Roman army move in a defensive formation like you describe? (genuinely curious if we have any documented evidence of that)
The Parthian border is not the only place where the Romans faced the problem - their centuries old and proven pattern of waging wars didn't properly work against the mobile armies with superior cavalry and missile troops on the ground favorable for cavalry and light missile troops.
Let's see how Julius Caesar solved the problem similar to that of Crassus:
The African Wars
on a sudden the enemy's horse began to extend themselves, and move in a lateral direction, so as to encompass the hills and weaken Caesar's horse, and at the same time to surround them. The latter could scarcely keep their ground against their numbers. Meanwhile, both the main bodies advancing to engage, the enemy's cavalry, intermixed with some light-armed Numidians, suddenly sprang forward, from their crowded troops, and attacked the legions with a shower of darts. Our men, preparing to return the charge, their horse retreated a little, while the foot continued to maintain their ground, till the others, having rallied, came on again, with fresh vigor, to sustain them.
Caesar perceived that his ranks were in danger of being broken by this new way of fighting, for our foot, in pursuing the enemy's horse, having advanced a considerable way beyond their colors, were wounded in the flank by the nearest Numidian darts, while the enemy's horse easily escaped our infantry's javelins by flight; he therefore gave express orders that no soldier should advance above four feet beyond the ensigns. Meanwhile, Labienus's cavalry, confiding in their numbers endeavored to surround those of Caesar: who being few in number, and overpowered by the multitude of the enemy, were forced to give ground a little, their horses being much wounded. The enemy pressed on more and more; so that in an instant, the legions, being surrounded on all sides by the enemy's cavalry, were obliged to form themselves into a circle, and fight, as if inclosed with barriers.
…the whole army … began to cast their eyes upon Caesar, minding nothing, for the present, but to defend themselves from the enemy's darts.
Caesar meanwhile, perceiving the enemy's design, endeavored to extend his line of battle, as much as possible, directing the cohorts to face about alternately to the right and left. By this means, he broke the enemy's circle with his right and left wings; and attacking one part of them, thus separated from the other, with his horse and foot, at last put them to flight. He pursued them but a little way, fearing an ambuscade, and returned again to his own men. The same was done by the other division of Caesar's horse and foot, so that the enemy being driven back, and severely wounded on all sides, he retreated toward his camp, in order of battle.
Chapter 18
Meantime M. Petreius, and Cn. Piso, with eleven hundred select Numidian horse, and a considerable body of foot, arrived to the assistance of the enemy; who, recovering from their terror, upon this reinforcement, and again resuming courage, fell upon the rear of the legions, as they retreated, and endeavored to hinder them from reaching their camp. Caesar, perceiving this, ordered his men to wheel about, and renew the battle in the middle of the plain. As the enemy still pursued their former plan, and avoided a closing engagement, and the horses of Caesar's cavalry had not yet recovered the fatigue of their late voyage, and were besides weakened with thirst, weariness, wounds, and of course unfit for a vigorous and long pursuit, which even the time of the day would not allow, he ordered both horse and foot to fall at once briskly upon the enemy, and not slacken the pursuit till they had driven them quite beyond the furthest hills, and taken possession of them themselves. Accordingly, upon a signal being given, when the enemy were throwing their javelins in a faint and careless manner, he suddenly charged them with his horse and foot; who in a moment driving them from the field, and over the adjoining hill, kept possession of that post for some time, and then retired slowly, in order of battle, to their camp. The enemy, who, in this last attack, had been very roughly handled, then at length retreated to their fortifications.
So, the Romans could solve such problems,
but...
1) It was post-Carrhae; it's pretty obvious that Caesar knew about disaster of Carrhae and definitely thought it over moving against a highly mobile army of cavalry and missile troops
2) A Roman army of Julius Caesar's general Gaius Scribonius Curio had already been annihilated here under similar circumstances, which gave Caesar some additional food for thought (
Battle of the Bagradas (49 BC).
3) With all due respect to Numidian horse and missile troops they were not a match for the Parthian mounted archers and heavy armoured cavalry.
4) Last but not least, Julius Caesar was a military genius, probably the most experienced and talented general on the planet of this time.
So, the idea, that an excellent infantry army might be easily defeated by the cavalry and missile troops finally stuck in the Roman mind, which helped Caesar to prepare and work out a strategy and tactics beforehand; Caesar probably enforced his legions with horse and missile troops and used them wisely.
But I am far from sure that if it had been Caesar who first met the Parthians on their ground he would have saved his army and his life.
And I am pretty sure that Crassus would have not.