First off, a whole-home surge protector is almost certainly NOT going to solve your problem.
I've had issues with my AFCI breakers tripping with large motor appliances (i.e. electric lawnmower, electric snow-thrower, mitre saw). This was in a brand-new build, so I was able to call them on it as a "warranty" issue.
The electrician came and swapped several of the AFCI breakers -- when the house was built a year ago, it was the first generation of AFCI that got installed. A few were updated to third-generation about 6 months ago, and there's now a fourth generation that I had them replace the rest with.
The third-generation AFCI, coupled with a decent surge suppressor power bar for the device seems to have eliminated the nuisance tripping. I haven't played with it to see if the power bar is still needed, but between those two things, the issue is resolved.
As for the "cause" of the AFCI being required now... that's up in the air. This is the first time I've heard of the blame being on the backstab connectors. Most seem to blame the idea that folks don't take care as to where they place nails and screws and a drywaller or homeowner ends up putting one right through the electrical wiring in the wall. The alternative theory (which is perhaps closer) is that it has to do with poor maintenance of device power cords.
I tend to believe it's the latter since our current code only required AFCI for (some) outlets and it excluded switch / lighting circuits and others like fridge and washing machine.