As far as I can tell immigration is not even on the table. This is what you want not what they want. The fact that they want to split their time between the UK and North America doesn't mean they will immigrate. Why is this even a discussion?
Because you cannot just come and live in Canada for part of the year without an immigrant visa, as has been explained more than once.
If you want to be in Canada, there are three status options: visitor, refugee, and immigrant. (I'll get to the diplomatic thing later.)
Visitors are specifically enjoined from effectively living here. If you rock up at the border with all your stuff and your cat packed in the back and appear to have rented an apartment, they will deny you entry. If you show up at the border with just a backpack but the computer shows that you've spent a suspicious amount of time in Canada in the last year, they will question you very closely about whether you're actually living in the country. If it is true that Meghan showed up without a return ticket, as has been reported, then the rules have already been bent for them.
Immigrants must fit into one of several established categories. I've posted a link. Most of them are job-based. The person who pointed out that Harry is a trained helicopter pilot is correct -- that actually is one of the occupations within the Skilled Worker program, HOWEVER, Harry could only get that if he was
actually working as a helicopter pilot. And the only place he'd be able to do that is in the oil field. I assure you that the Duke and Duchess of Sussex are not going to be settling in Fort Mac. Whether he'd be able to earn enough points is an open question since he hasn't been part of the Army Air Corps since 2013 and they'd likely have to stretch the definition of "recent skilled work experience" to give him any points in that category at all.
As for the diplomatic visa option, the guidance suggests "a senior official of a foreign government, travelling on a diplomatic passport, should not be issued a diplomatic visa if the individual intends to enter Canada for commercial negotiations with private enterprises, or on a private visit. " Which means, again, they'd have to bend the rules.
In short, there is no way that allowing the Sussexes into Canada to kinda-sorta live here much of the time can be accomplished without bending the rules. So why does that matter?
We are currently a country that 1) is dependent on skilled immigration and 2) operates some of the most liberal refugee programs in the world (for instance, we're about the only place where we have a program set up to allow private citizens to sponsor refugee families).
However, we're also a country with a rather tense balance between conservatives and liberals, as can be seen in our last election. Immigration policy is one of the areas of a split in opinion. We need immigrants, but in order to maintain a robust immigration program, it must be seen to be fair and working in good order.
Breaking the rules, in a very public way that screams "not fair, not working in good order", to satisfy the whims of an incredibly privileged pair who could easily just go to the US without breaking the rules just doesn't sit well with me, I'm sorry. And, honestly, I'd rather have a few more doctors.