Why did Mettius Fufetius not join the Veiites in directly attacking the Roman King Tullus Hostilius?

According to both Livy (died circa. AD 17) and Dionysius of Halicarnassus (died after 7 BC), Mettius Fufetius's intention was to observe how the battle went and then join the winning side. In doing so, he was prepared to betray both sides for he had made promises to both the Romans and the Etruscans.

Livy attributes this prevarication to a lack of courage. However, it should be noted that we are dealing with semi-legendary accounts and that we have no way of verifying such details as how large the respective armies were. The supposed events took place almost 600 years before either Livy or Dionysius were born, and their original sources are lost to us.

When Tullus Hostilius, legendary 3rd king of Rome, had to face an Etruscan attack (comprising of forces from the cities of Veii and Fidenae), he called on the vassal state of Alba Longa to join him in battle. Led by Mettius Fufetius, the Alba Longa army was assigned the right wing, facing the Fidenates while the Romans took the left against the Veientines. Then, according to Livy,

The Alban commander was as wanting in courage as in loyalty. Not daring, therefore, either to hold his ground or openly to desert, he drew off by imperceptible degrees in the direction of the mountains. Then, when he thought he had got near enough to them, he brought up his whole battle-line to an elevated position, and still irresolute, deployed his ranks with the object of consuming time. His purpose was to swing his forces to the side which fortune favoured.

(my emphasis)

When the battle commenced, the Albans withdrew to a nearby hill and waited to see which way the battle would go. Initially, according to Livy, it seemed that that the Etruscans would win as the Roman right wing was swamped, but Tullus rallied his forces, sowed doubt among the Etruscans as to the Albans' true intentions, and won the battle.

Dionysus' account includes a long speech attributed to Mettius Fufetius in which Livy's account is basically 'confirmed', with the added detail that Mettius hoped and expected that the Etruscans would win so that the Albans would no longer be subservient to Rome (he uses this to justify his betrayal of the oath to Rome):

...if this enterprise turns out according to our wish, as is reasonable to expect, the Fidenates and the Veientes, in delivering us from a grievous subjection, will feel grateful to us, as if it were they themselves who had received this favour at our hands.

However, should the Romans be winning, Mettius had a backup plan:

When the Alban observed that Tullus had already won a brilliant victory, he also marched down from the heights with his own troops and pursued those of the Fidenates who were fleeing, in order that he might be seen by all the Romans performing some part of the duty of an ally; and he destroyed many of the enemy who had become dispersed in the left.

According to Dionysus' account, Mettius was opting for what he thought was a low-risk strategy. Also, Mettius' reputation at Alba Longa was low because of the Horatii vs. Curiatii defeat which had led to the Alba Longans' subjugation to Rome. States don't typically approve of heavy casualties so Mettius' strategy would achieve several aims:

...without sharing in the dangers of either side, we shall have a part in the good fortune of both.

Unfortunately for Mettius, Tullus' suspicions of the Alban dictator's actions were confirmed when captured enemy leaders revealed that Mettius had been conspiring with the Etruscans, encouraging them to march against Rome. Mattius' punishment was gruesome. Livy's account is as follows:

Then Tullus said: “Mettius Fufetius, if you were capable of learning, yourself, to keep faith and abide by treaties, you should have lived that I might teach you this; as it is, since your disposition is incurable, you shall yet by your punishment teach the human race to hold sacred the obligations you have violated. Accordingly, just as a little while ago your heart was divided between the states of Fidenae and Rome, so now you shall give up your body to be torn two ways,” He then brought up two four-horse chariots, and caused Mettius to be stretched out and made fast to them, after which the horses were whipped up in opposite directions, and bore off in each of the cars fragments of the mangled body,83 where the limbs held to their fastenings.

Other sources:

J. D. Noonan, 'Mettius Fufetius in Livy'. In Classical Antiquity 25(2):327-349, Oct. 2006

Livius.org, 'Titus Livius or Livy'