Wouldn't that be nice. Now consider the case of a pharmaceutical company that has to spend hundreds of millions of dollars to develop a new drug and get it past FDA. If there is no IP protection would you as the CEO of this company spend that kind of money on innovating when the resultant drug could be copied a week after it appears on the shelves? In this case you would be competing on product alright - exactly the same product. But the copier has had no R&D cost and can undercut you and put your offering out of business.
The issue is often framed in terms of all patents being bad, or all software patents being bad but to anyone to gives the matter more than the kind of superficial thought stemming from ideology the reality is rather more complicated.
Pharmaceutical and other physical patents make sense and appear to work. But arguing that software companies won't innovate without patents ignores the fact that software companies did innovate without patents, for years. And software patents obviously haven't been working: see Microsoft's patent on "if not", among other things.
You are absolutely correct. There are differences between the two industries. The two key ones would seem to be that (a) the investment required in time and money to create the software and its likely lifetime value are low compared with a drug, and (b) the ease of difficulty with which the software may be copied can vary a great deal. Compiled source code is harder to reengineer than a drug. Server side code that is held as a trade secret, such as google's search algorithms, is hard to recreate. So in these cases it is quite true that there has been innotation (ignoring the fact google did have some IP protection). But there are cases I can think of where it would be downright foolish for a software company, particularly a small one, to invest substantially without protection. The key characteristic is that the code cannot be held secret and can be readily read and thereby copied. The key point is that it really isn't very helpful to generalize to broadly about the software industry.
The issue is often framed in terms of all patents being bad, or all software patents being bad but to anyone to gives the matter more than the kind of superficial thought stemming from ideology the reality is rather more complicated.