1) I've been doing pretty much exactly what you've proposed since 2016, albeit mostly with small buildings projects and delegated design stuff.
2) I've never had to file taxes in any of the US states in which I've worked. In a nutshell, I believe that you only have to file taxes in jurisdictions where you have a physical/legal presence. Simply working on projects in a particular jurisdiction doesn't trigger a tax burden in that jurisdiction in my experience.
3) Inspection requirements have been largely unproblematic. Where requirements are minimal, it's at my discretion. Where the requirements are hardcore special inspection stuff, it tends to be pretty easy to line up a 3rd party inspector. I could see this being tricky for temporary works stuff though.
4) I anticipated that getting US coverage for my Canadian insurance policy would be a hassle. I was pleasantly surprised to find that was not the case. I basically have the cheapest policy that it is possible for an engineering firm to have and my US work didn't affect the economics of that at all. Big insurance firms are accustomed to working across borders in a way that small fish engineering firms are not it seems.
5) You do indeed need to figure out the Certificate of Authorization business for each state which can be annoying. Depending on where you're doing work, you may need a certificate of authorization, the equivalent of a permit to practice, or to be registered with the state department of commerce. Or some combination of those things. In this respect, I wish that I had set myself up as a sole practitioner rather than as a corporation. Many jurisdictions give sole practitioners a break on this stuff and it would have been nice to have been able to avail myself of that.
6) Different states can vary wildly with respect to how helpful they are towards foreign engineers attempting to do business in their jurisdiction. Wyoming was so kind to me that I'm half tempted to move there. Illinois has treated me so badly that I half wonder if there's someone living there by the same name as me who's on the registered sex offender list or ten years behind on child support.
7) In general, I agree with your strategic thinking on this. I've done very well on my US work which offers three advantages for me:
a) The exchange rate.
b) The size of the markets involved. I've done the best in very populous states that have the SE requirement like California, Illinois, and Florida. California alone is as large of a construction market as Canada is.
c) There are some Canadian component suppliers who value a relationship with a local engineer who can also take care of their US work. For this, it is advantageous to be able to stamp work in a LOT of US jurisdictions if possible. I loosely team up with a few other engineers for this purpose in order to get greater coverage without having to get all set up sparsely populated states for one off assignments.