Yeah, don't do this in Canada, or the professional engineers association can come after you. Only certified members of an engineers professional association can use the title.
To be clear, it is illegal, for example, to pass around business cards that say 'Software Engineer' if you're not certified.
As an amusing example, in the province of Ontario, people with the Microsoft Certified Systems Engineer certification are allowed to use the title 'MCSE', but not its expansion, because it contains the word 'Engineer'.
However, you are always allowed to state your degree, so you can say, {name}, B. Eng., or M. Eng., as the case may be.
*At least, in Quebec and Ontario - the legislation is province-scoped, I assume other provinces are similar.
Coming from a US perspective, I feel like "engineer" on its own is a descriptive word. "Professional Engineer" is a trademarked title, and that seems reasonable. Do I have certification as a PE? No. Do I think it's reasonable to describe what I do as software engineering? Yes. To me, it implies that I take part in planning, designing, implementing, supporting, and retiring software. "Programmer" connotes that I took someone else's design, wrote to that spec, and handed the results off to someone else, rather than taking part in the entire lifecycle.
It's not a requirement for ME and EE, but it is a universally recognized certification. PE-licensed engineers often enjoy better employment prospects.
(FYI, there is PE exam for software. The difference is: it's not widely know in the industry.)
I tried to see if there was an opportunity for an engineering mentor at my job (One of the big four) and I was unable to get anywhere. It seems that it is better for our job prospects to get a job at a prestigious/interesting company and gain experience there than try to go through the licensing process.
Some engineering fields have all those things you describe but it is usually because there is a high degree of physical risk to the public, like structural engineers for example.
Mechanical and Electrical engineers, for example, at most companies are hired without any such certifications, unions, oversight, or any of what you've mentioned. I have a degree in EE and CS and have worked in both fields doing everything from IC design to app development and the hiring process, oversight, etc has been the same in almost every case - no membership or union required. I have friends who work as ME, Chemists, physicists, etc and the same is true for all of them except in the exceptional cases where they are working on a medical device or something.
Really all those things you mention at most companies for most fields of engineering come down the the company culture itself and the technical leadership at those companies.
The really funny thing about your take is that in most cases I find that high level software developers have a much stronger cult of engineering excellence that any of those other fields. If you saw the "process" most EE's used to ensure high quality engineering at large companies like Intel you would be horrified. And definitely don't ask those EE guys to write any code, it will almost certainly be terrible.