You can try a different reasoning track. In the 'old days' software was more often than not driven by intrinsic motivation. I just loved making games that me and my friends could play. I loved writing software so writing useful apps for myself and good people around me did not need an extrinsic financial reward. Later I worked in academia for a long time. Again the research. gaining new insights in the company of other passionate and smart people was the intrinsic driver.
It was not until much later, due leaving good environments for bad reasons, that external financial motivations became a driver, providing a temporary bad self justification for not leaving sooner. Even then, solving the puzzle, exceeding the clients expectation. We're still the most rewarding parts of the job.
If you love what you do, money just becomes an issue in just 2 cases.
(1) When your needs for living in comfort (and with that I mean the luxury of not having to worry about money) are not met.
(2) When you feel others are exploiting you financially (you see disproportionate gains by others based of your work)
Now. Against this background, let us return to the question of 'will software still get written if we allow the free distribution of it'?
My believe is yes. While it is most certainly not for everyone, a certain type of people just love to create digital platforms and solutions. In fact their passion is now more often than not exploited, see for example the practices in the major gaming industry. There are more than enough specific needs that people will want to prioritise to offer financial incentives for their prioterization even if that means the result will become part of the commons. Current exclusive IP exploitation rights very seldom reward the creators, most often just those who have constructed layers on layers of financial instruments confining and leeching of the creative.
Finally IP protection most certainly stifles innovation. It restricts forms of further creation. The question is Wether this reduction is compensated by a boon in extrinsic driven creation that would be missing in the absense of guaranteed monopolies on exploitation. My guess once again is no. Science, innovation in knowledge, has progressed for centuries through the free sharing of ideas. The Eastern electronics industry has thrived in a climate of fluid copying and absense of IP enforcement. Most of the 'major' industry investments carry disproportionate public investments through grants and incentives while still locking up all rights on the publicly funded results.
We might see a different software world if copying and extending of all software was free, but not one whete creators go hungry, or innovation ceased to exist.