SLKR being OP (with our without his ultimate) against regular teams is kind of the point. He's a GL, therefore he's supposed to be tiers above most teams (at least until DCs come into play, but that's a separate issue).
Thematically, SLKR's kit makes sense. He doesn't care that much about the First Order, he just sees them as a means of becoming more powerful (and getting revenge against Luke). Gameplay-wise, especially against other GLs? Look at JMK for example. SLKR has very few survivability mechanics, and the ones he does have (boosting the team's max health and protection) are nullified because of JMK and his leader ability. SLKR's ultimate charge is based on the team landing hits, especially critical hits, against the enemy, which is decreased severely against JMK, who gives critical hit immunity to anyone who has protection up, which JMK grants at the start of the battle, through his DI special, and through his ultimate (which charges incredibly fast compared to other GLs). SLKR's kit focuses mainly on offense and very little on defense, while JMK is crazy when it comes to defense and very good when it comes to offense, especially since he has ways of partially or completely (i.e., allows the whole team) to ignore taunt, and once they start targetting SLKR it's over. Look at Jabba as another example. Boushh disables all assists on your characters for a few turns, which severely decreases the amount of charge you get toward the ultimate. Meanwhile, they assist like crazy, have decent survivability mechanics (Jabba inflicting Blind and granting Protection up on his basic, protection recovery once his contract is fulfilled), deal lots of damage (especially when Boushh uses her special while you have TDs). Another example, JML. Like I said earlier, SLKR relies on critically hitting the enemy, which is practically disabled when JML uses his AoE to ability block and slow down your team while also granting critical hit immunity to his own, after which JKL stuns everyone but SLKR, further decreasing your progress toward the ultimate. And depending on the enemy team comp, they have good survivability (e.g., HYoda, Shaak-Ti) and decent damage (mainly through Luke's granted ability), they reach JML's ultimate fairly quickly, and once that happens the entire team ignores taunt, while Luke himself is able to use his specials back to back, which dramatically hinders your chances of even partially reaching the ultimate, let alone completely filling it up.
TL;DR. There has to be at least some balance. SLKR is a powerhouse as he continues siphoning mastery, but has the survivability of a wet paper bag compared to other GLs, especially when said GLs have ways of hindering or outright disabling the things that allow SLKR to become a powerhouse.