IANAL, but yeah, part of taking somebody to court is making sure that they have the relevant paperwork in their possession (service of process), which is part of “due process”. Defendants have to have the information about the claims against them and when/where they’re expected to be in court.
No, I don’t understand either why somebody would try to avoid service of process for a court case they know full well is coming their way. It doesn’t enable you to avoid the charges against you, just makes the process more complicated and possibly more punitive.
But I have pretty much given up trying to understand why the hell Giuliani does anything.