Erm, it very much isn't illegal. At least not in most places.

Taking on fresh debt to pay off other debt is the very definition of a consolidation loan which is perfectly legal in most, possibly all, jurisdictions.

There are limits of course, like not using a loan to pay the deposit on a mortgage, or simply not lending beyond defined means, but these are set by the bank to manage their own exposure to risk rather than limits set by law. Such limits are merely encouraged by law, via regulatory limits on standing capital compared to debt held and so forth.