There is at least one military historian (Alexander Zhmodikov) who argues that we should interpret Roman warfare as something like that: primarily skirmishing at range with javelins, with the sword-charge as a last resort, with the sword-charge occuring as a last resort (but one often decisive in breaking morale) akin to the bajonet charge of the 18th-19th century. (It is perhaps not entirely coincidental that this historian also wrote on Napoleontic warfare.)

You can read his article here: https://www.jstor.org/stable/4436566?seq=1

This view has not met with universal acclaim. Most of his colleagues would argue that Zhmodikov goes too far in his reinterpretation of the evidence, and that melee shock combat played a larger and more decisive role than he allows for. Some (Wheeler, Firepower: Missile Weapons and the Face of Battle, 2001) take an entirely opposed approach. See also Wheeler's older "the legion as phalanx" article from 1979. He's written more recent follow-up articles "the legion as phalanx in the late Empire" in two parts, which unfortunately I have not read.

It is telling that there is so much confusion about just what a Roman legion looked like and how it fought. There are depictions of maniples as rigid shield-walls, or as loose "clouds" of men grouped around standards. (see for example Lendon, Soldiers and Ghosts page 179 for a nice illustration. Can't find it only unfortunately.) There are cases to be made for both.

An interesting article on the topic available online is M. Taylor Visual Evidence for Roman Infantry Tactics

I personally find the interpretation of battle with a greater emphasis on skirmishing and missile exchanges to be quite convincing. Zhmodikov probably does go too far, and there are too many counter-examples that indicate sword-combat did occur and did prove decisive, but putting more emphasis on all those javelins the Romans carried is a welcome corrective to a historiography that has largely ignored them or reduced them to a footnote. But I am an amateur in this debate, so take that with a grain of salt.

u/Iphikrates will be able to tell with much more expertise how skirmishers and light infantry could also be decisive in Greek warfare, even if the phalanx itself was a purely melee outfit. See for example here for why this was, and here on how they could fight.

There are a few reasons why missile warfare is given little emphasis in our sources. Firstly, in most ancient cultures the light skirmishers are the low-status troops. The elites, who are writing and reading the literary sources, fight as armoured cavalry or heavy infantry. When Caesar writes his commentaries he is always stressing the exploits of his centurions. Quite likely these men were doing a lot of exploits, but also quite certainly they were more important politically than his auxiliary archers or cavalry, whom he sometimes mentions as a group but never bothers to single out as individuals.

Secondly, even if missile exchanges did form a much bigger part of ancient battles than we assume, it remains true that they only very rarely DECIDE the battles. Even in the 18th century, bayonet charges could instantly break an enemy where hours-long artillery and musket barrages could not. (Though I'm admitting we're getting outside my area of expertise here.) And Zhmodikov's skirmishing hastatus is not a pure ranged combatant either. He remains capable of engaging in melee combat, with body armour and a big shield.

Ancient missile weapons were far less effective than 18th century muskets and cannon, and ancient body armour and shields were much more effective at defending troops than 18th century hats and coats. Our sources make a cliché about soldiers being "covered in wounds" as battle progresses, but they seem to take it for granted that these wounds (probably on exposed limbs) did not impede them enough to stop them from fighting.

Conversely it seems ancient soldiers were more willing to engage in melee combat than 18th century soldiers were, (19th century sources stress how rarely actual bayonet combat took place, but ancient sources claim the opposite about combat with sword and spear, only occasionally mentioning enemies breaking and fleeing before any combat took place.) This probably was because ancient shields and armour made this combat a less frightening and risky prospect than it would be for an unarmoured musketeer.

Finally, there may well be a cultural dimension in play. Battles in ancient times were fought for a reason. There was something to defend or attack. Armies had to offer battle by leaving defended camps and taking up a position that was not so strong the enemy would not dare attack it. Then the enemy could be engaged and hopefully defeaten in a decisive manner and bring a war to an end.

An army of light skirmishers would typically not be able to hold a field. Without the advantage of tactical mobility cavalry possesses, they would not be able to evade a more aggressive enemy (let alone enemy cavalry) without fleeing the field altogether, unless the terrain heavily favoured them. And an army that just ran away at the first enemy onset would hardly be considered much of a threat and their enemies would just assume they had won the battle. Essentially, to fight as light skirmishers only, you would have to change to a kind of guerilla warfare. And that is concededing much of the victory to the enemy before the battle has even begun.