4 cm is almost 2 inches. That's a whole lot. It also means that the top tube and head tube are going to be bigger so the bike is going to look goofy when you get it adjusted to where you can ride it.
There's also this: It takes every bit as much time and money to build an ill fitting bike as it does to build one that fits right.
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My greatest fear is all of my kids standing around my coffin and talking about "how sensible" dad was.