There are no legit software patents,
That's easy to say in the abstract. What about Google's PageRank patent? Search was a hard problem for many years. Altavista, etc were mediocre. Google came up with a new approach that was leaps and bounds better. In other words the very definition of a useful new invention. So you are left with two possible arguments why it should not be patentable. Either (1) Google's innovation was obvious such that anyone in the field would have known about it or (2) software inventions as a whole are undeserving of patents.
(1) - If you say it was obvious, then that means some other software creations are not obvious. Whatever those non-obvious software things are would pass test (1). To deny those things a patent you must invoke (2).
(2) - Why doesn't any software deserve a patent? Is creating a great, new, non-obvious piece of software somehow less work than a mechanical invention? Doesn't it require just as much genius, study, insight, and effort to produce a new search system as a new fishing hook or screw design? Software has the potential to be vastly more complicated than any other type of machine. An airplane has tens or perhaps hundreds of thousands of moving parts which must be synchronized. Large program can easily have millions of lines of code performing tens of millions of operations that potentially interact. To say that software is per se not worthy of patenting draws artificial and illogical distinctions between the tasks involved in software and mechanical arts.
Software is NOT purely mathematics, any more than a nuclear bomb is purely quantum mechanics. Functional software has to account for a plethora of real world conditions. How much processing power is available? Storage space? How quickly do we need a result? Are quick partial results better then slow complete results? Does our input data change, and if so how frequently? How do users interact with the system? These and numerous other considerations have to be considered even at the algorithmic level. Just because it all runs in binary boolean logic somewhere doesn't make it all mathematics. The system encodes many other considerations that don't show up at that level. For the same reasons, software can't be dismissed as purely "abstract ideas" or "mental steps". Theoretically you can simulate a game of Doom with bit logic in your head. However the results aren't remotely comparable to playing the game in real-time on a computer.
Now we can quibble over exactly where to draw the lines to get a software patent: how inventive it must be, how narrow the claim coverage is, how much protection it should afford, what the public domain already contains. Those are all legitimate questions. But to dismiss all software out of hand as being inherently unpatentable is nothing but illogical prejudice.
and quite a bit of planet sees it that way.
Can't argue with that. Whether that's desirable is left as an exercise for the reader.