Many people assume the KJV is "the true Bible" not because of any objective reason, but because of familiarity with it. They are familiar with and may have memorized the wording of many of its passages. Someone comes along and reads a different translation, and those familiar with the KJV will compare the new version to the KJV. Any difference from the KJV may be perceived as "incorrect" or even "corrupted". Now consider the reverse: someone grows up with the ESV, becomes familiar with it, and memorizes many passages. Then someone comes along and reads a familiar passage from the KJV. The ESV reader will have every reason to think that the KJV is "incorrect" or even "corrupted". The flaw with this reasoning is in overlooking the fact that both the KJV and the ESV are translations, and not the originals as penned by Paul, Peter, and the others.
The KJV was translated primarily translated from seven printed Greek editions, not directly from manuscripts. The translators checked then-available materials such as earlier English versions (from which the KJV draws heavily), and some foreign-language versions. Now, there are almost 6,000 manuscripts available for the Greek NT, and a great many in other early languages, that were simply not available for examination in 1611. Most modern translations, including the ESV, were translated with reference to this much larger body of source material.
Where a passage contains certain words in the KJV that aren't found in the ESV, you can be certain that there is a good reason why, even though you may not agree with the reason. Most of those "missing" words can likely be found in footnotes. The reality is that they aren't "missing" at all; the translators made a decision that those words don't belong because they probably weren't in the original text. There are words and entire passages whose provenance is questionable; there is scholarly debate on whether such words were actually written by the author of that text. 1 John 5:7 is in this category. The KJV also contains a great many words that weren't in the original languages; the translators added them for one reason or another. Most of these are printed in italics today. Should we toss the KJV because there is so much "added" to the text?
Instead of assuming that words not present in the ESV were "deleted", assume that there are differences in source material and that the scholars who do the challenging work of translation are doing their best to present a sound, accurate, and reliable text. Differences are just that - differences. You'd have to look to the JW's and Mormons to find intentional corruption of the biblical text.