As others have pointed out, Varan would've had a good shot at having Mothra's role and by default that means Anguirus would've had King Ghidorah's role. But with that in mind, I suspect Anguirus wouldn't have had much of a "lead" role among the three monsters and it would have been more of a battle between Godzilla and three more or less equal monsters. I've been critical of KG being a "good" monster even if I love the movie, but I much prefer the three monsters we got anyhow.
While GMK's monster roster is a point of debate, we do understand why Toho went with those three. Baragon, Mothra, and King Ghidorah all have performed well in Toho's favorite monster surveys among the Japanese, so why not cash in on monster with big appeal?
Had they hired a idiot like me, I'd have been fine with keeping Mothra but used King Caesar instead of Baragon and used some other dragon monster. Try something new, ideally. It doesn't have to look anything like this, but Matt Frank's beautiful work shows a beautiful and majestic yet aggressive looking fire dragon could've worked well.