If you change tire sizes the gear ratio will be off and you'll break something. That 20% difference isn't in gearing, it's referring to the amount of slip the rear wheels need to activate the awd.
And no, it's not a design problem. There's something wrong with yours. If it was working properly, then it should engage and disengage without you even noticing, and like I said earlier, almost instantly when the rears slip.
You also mentioned locking the front. Yes, other machines can be manually locked into 4wd, and like you said, it's hard to drive them while locked, and you have to stop to disengage it. The polaris awd design also completely locks the front wheels when it engages, but only when needed, making it easy to steer. That's why it's the only true AWD system made. Unless it has a full locking diff, other brands only give you 3 wheel drive.