I would argue that most classes -- Barbarian, Druid, many Clerics, Monks, Rangers, some Rogues, and many Wizards are just as "bad" at social interaction as the Fighter. (Not just champion; none of the martial archetypes contribute very much to social interaction.) That's over half the classes. Therefore, these classes are not
weak, they are
baseline. The more social classes (Bard, Paladin, Warlock, Sorcerer, and certain builds of Cleric, Rogue, or Wizard) have special benefits that take them above and beyond, but that doesn't necessarily make the other classes incapable of social interaction.
As to your initial question: Every class has a way to deal
damage that scales by level:
- Warrior-types get Extra Attack. Fighters keep getting more attacks; Barbarians get more rage benefits; Monks get more ki points; Paladins get more smite (plus constant +1d8 smite); Rangers get... well, something.
- Rogues get sneak attack.
- Spellcasters get higher level spell slots, and cantrip damage increases. Some clerics also get +1d8 damage to weapon attacks at certain levels. Many spellcasters eventually get to add their ability score bonus to certain spells and/or cantrips (or in the case of Blade Warlock, to weapon attacks).
Beyond that damage scaling, every class contributes to combat in different ways. Classes that are "weak" in the combat pillar (like Land Druid, Lore Bard, certain Cleric domains, most Rogue builds I've seen) still keep up with damage scaling. Classes that are "strong" in the combat pillar (Fighters, Paladins, Evoker Wizards, certain Cleric domains, Moon Druids at certain levels) get that way by having better defenses, awesome area attacks, healing/buffing, or battlefield control.
So my advice for your hypothetical low-combat prestige classes: keep up the damage scaling. (And obviously don't go below d6 hit die.) That's the "baseline" for combat effectiveness. If your classes don't get any combat ability above and beyond that, they'll still be able to contribute meaningfully during a fight.