You "can" play it every other day. However you will miss out on daily activities, daily bonus energy boosts and most probably lose arena ranks (which gives crystals for energy refreshing+purchaseable gear) a lot, which in turn makes your player level progress awfully slow if you chose to play that way.
It chains all together and creates a domino effect, slow playerlevel progress, your characters stay low level+geared, they can't stay competitive in arenas. Most important of all you would need a lot more time to broaden your character roster and gear them up for battles. If you just enjoy doing lightside+darkside+cantina+galacticwar and not too fussed about arena, it's definitely playable, but you will progress very very slowly. Is it playable and can you find your personal joy with it? Definitely.
Most players would say being topdog in arena is the only real goal and purpose of the game, but that's not entirely true. There are only so many spots in the pvp scoreboard to occupy and many players have other self-declared priorities/goals ingame.