Let's for a minute say that the "accidental" galaxy destruction is a viable method of attack. Because quite frankly it isn't even close to my main point of contention.
First, consider that for normal sized people, in most cases, an opponent has to aim for his opponent and close whatever distance with his attack at minimum to win. Let's say that at a maximum this distance would perhaps be 1.000 feet.
Now, let's say that STTGL is 1 billion light years tall (I really don't feel like doing the math to come up with an accurate number). Now assuming that we have to have a clear start to the battle, STTGL has to start about at least an arm span (0.5 billion light years) to prevent destruction of the galaxy before the fight even begins. Well, it still has to close that gap. And even though it can swing his arm (or drill) at speeds to close that gap in the same timeframe your average giant robot can launch an attack the length of his armspan, it still takes the same amount of time to actually launch said attack.
In other words, distance is linearly proportional to speed, and SSTGL still has cover a distance relative to its own size.
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"One toot on this whistle will take you to a far away land."
-Toad, SMB3