I saw an application re-architected within 2 years of its introduction into production, and others rewritten in different technologies (one was C++ - now Java). Both efforts were were not, to my mind, successful.
I prefer a more evolutionary approach to bad software. If you can "componentize" your old app such that you can introduce your new requirements and interface with the old code, you can ease yourself into the new environment without having to "sell" the zero-value (from a biz perspective) investment in rewriting.
Suggested approach - write unit tests for the functionality with which you wish to interface to 1) ensure the code behaves as you expect and 2) provide a safety net for any refactoring that you may wish to do on the old base.
Bad code is the norm. I think IT gets a bad rap from business for favoring rewrites/rearchitecting/etc. They pay the money and "trust" us (as an industry) to deliver solid, extensible code. Sadly, business pressures frequently result in shortcuts that make the code unmaintainable. Sometimes it's bad programmers... sometimes bad situations.
To answer your rephrased question... can code maintenance costs ever exceed rewriting costs... the answer is clearly yes. I don't see anything in your examples, however, that lead me to believe this is your case. I think those issues can be addressed with tests and refactoring.