For the most part, missing sub-classes aren't a big deal. A 3pp player-focused product should be about adding new options, new classes, new sub-classes, etc, not old ones. But, a few sub-classes have unique mechanics that could have other uses, and could have been a better choice for inclusion. Going with Champion rather than Battlemaster, for instance, means CS dice and maneuvers are out of bounds. Which is too bad, they had a lot of potential to 'build off,' either to add more meaningful options for the Battlemaster at higher level, or to expand into more interesting martial classes. The last UA used variations on CS dice in two fighter sub-classes, for instance. A 3pp couldn't do anything similar, with just the Champion to work from. Same goes for Wild Magic, it's only found in the missing Sorcerer sub-class, but it has a lot of potential uses - magic items, artifacts, magical accidents, chaos zones or whatnot - D&D magic is usually very dependable and predictable, locking away the best example of the opposite we have in 5e is unduly limiting. I suppose the Wand of Wonder could always be an alternate starting point for that though.
Backgrounds, OTOH, don't seem like a problem. Can't use the Soldier background? Substitute an Officer or Legionnaire or Mercenary or Militia background.