I don’t agree. If anything right now we have the opposite problem where the English world for instance pretty exclusively uses a more than 500 year old translation of the Bible, despite much more modern-English versions being translated from some very early Greek versions of the texts (therefore being more readable and less telephone-y). The reasons for the KJV being preferred are many but none make any real theological or linguistic sense.
What really happens though is not so much a game of telephone than the fact that every culture gets to decide on its own (usually provably incorrect and inconsistent) interpretation of the texts, because the whole thing is so internally inconsistent it’s basically a Rorschach test no matter which way you translate it. Progressive Christians will basically tell you that literally none of the Old Testament is to be taken literally which… okay? Extremists sects will do the opposite. Then there’s the whole dogma around Lucifer and Hell, whose existence is clearly an inconsistent amalgamation of old polytheist religions and no matter which way you read or translate it doesn’t translate to the Lucifer or Hell that most Christians ever think about when they say “Lucifer” and “Hell”. That part was just straight up made up over the centuries because it was a convenient scarecrow, yet is is absolutely load-bearing to the dogma of almost every Christian sect. And let’s not even get into the feminists and queer people who’d put Simone Biles to shame with their mental gymnastics justifying the Bible being an Ally, Actually™. That’s not a game of telephone, that’s just Weapons of Mass Denial.