The Military uses of the Palantiri.

[Inziladun]

I think there is too little detail about the Last Alliance and their deeds during the Second age to say the Palantíri weren't used for tactical or strategic planning. In fact the military victory over Sauron might seem to support the fact that they were. In fact, due to their use:

Thus the Númenóreans were aware of many things that their enemies wished to conceal, and little escaped their vigilance in the days of their might.

Silm Of the Rings of Power and the Third Age

'Númenóreans' there must refer to Arnor and Gondor. The Stones had been given to Amandil, father of Elendil, by the Eldar in Eressëa during the last years before the Downfall, and the Faithful in Númenor, who were led by Amandil, were far from being 'in the days of their might' at that time.

The Stones would have had limitations, however. The minor Stones were smaller, and were the ones with fixed 'polarity', in that they would only work when the surveyor was looking at the face which corresponded with the surveyed direction. That would seem to make them unsuitable for use 'in the field'.
Conversely,the larger ones, such as the Stones of Amon Sûl and Osgiliath, lacked the fixed orientation, but were probably too large and heavy to be practically carried into a battle situation.
If the palantíri weren't present on the actual field of battle, I would think issuing orders to troops that were based upon knowledge gained from them to be somewhat problematic.

In the Third Age, Arnor and Gondor did communicate with the Stones, both with one another and within their own realms.
Arnor, however, quickly became divided into the three smaller kingdoms, Arthedain, Cardolan, and Rhudaur (around the year 861), and they were unable or unwilling to unite against the Witch-king when he appeared around the 1300's.
Gondor also, fell victim to internal wars with the Kin-strife, beginning in 1432 (in which the Stone of Osgiliath was lost in the Anduin).
Arthedain probably used the Stones of Amon Sûl and Annúminas to coordinate its defenses, but I think they were simply overpowered by superior numbers.
As well, Gondor likely made use of the Stones of Minas Anor and Orthanc for military purposes for many years before the fall of Arnor. The Tale of Years shows them defeating the Men of Harad, the Corsairs of Umbar, and the Wainriders at various times before Minas Ithil was captured.