Why would Rome want landowners to join the army?

Before the introduction of a professional army, the Roman infantry was a militia of peasant-proprietors and not of the wealthiest landowners, who joined the cavalry. This is said to have been the result of a military reform by the sixth king, Servius Tullius (r. 578-535 BC) which is thought to have been linked to the introduction of the new Greek hoplite phalanx (wing) formation. Hoplites were soldiers with heavy armour which fought in tight formations. They were supported by light infantry men (velites). The former were called the classis and the latter the infra classem (class below) and were defined by the value of their property, with the richer ones being the hoplites as they could afford the heavier armour - soldiers had to provide their equipment. The reform also had political aspects.

The propertiless (proletarii) very probably exempt from the levy right from the beginning of Servius Tullius' reform and this might have been part of his pledge to lighten the burden of war on the poor which he identified as a prime cause of indebtedness among poor Romans. The soldiers were rewarded for taking on the burden of their duty as citizens to defend Rome (which included, besides expenses, time spent campaigning and risk to life and limbs) by giving the more political weight through the creation of the assembly of the soldiers (comitia centuriata) which had the right to vote on important state matters. This , at this time, made the constitution more populistic, gave the intermediate classes a stronger political say, and created a counterbalance on the senate which was dominated by the wealthiest men.