In a nutshell, internalized objectification is a cognitive process (like everything else), and it consumes mental resources. When these cognitions are made accessible by dressing participants in revealing clothing (swimsuits in most of these studies), those participants perform reliably worse on a wide array of cognitive tasks (arithmetic, simple logic, various other tasks that have been previously used in cognitive psychology literature) than participants in less revealing clothing (usually sweaters).
Basically, if a woman is thinking "I look fat in this swimsuit," she is taking mental resources away from every other process.
Common sense is not a reliable indicator of reality. Many things (general relativity, quantum physics, Milgram's obedience experiments, the representativeness heuristic, the conjunction fallacy, etc.) contradict common sense. If you prefer common sense to empirical science you will be reliably wrong on a wide array of things. I would urge you to banish the phrase "common sense" from your mind if possible.
Can you summarize the evidence more verbosely? Only 1 of those 5 references could be easily followed (1 broken, 2 for-pay, 1 no link). I couldn't find evidence for your claim in the one working publication and it kind of goes against common sense.