Here's my take - my kids are notorious for taking OFF their shoes, so I will more easily accept the slightly harder soled shoes easily. I know my kids well (like myself) and I know the amount of time they spend in shoes is minimal. There are probably days they don't wear any. I spend the most time selecting shoes they will wear for longer amounts of time (like when dd1 is in school, we select a better sneaker than for something she'll wear for half her time playing outside. I'll get something cheap or just pretty for that.). We also check whether all their shoes fit together some evening every 2-3 months (so I know which ones they're about to outgrow - cause if they like something enough, they won't always tell me it's getting small).
How much time does your child wear their shoes? Do you wear them in the house? Where and how often are you walking around outdoors? And for how long? Those are the kinds of questions I personally consider when selecting shoes for my littler kids.
For young kids, I also would check whether I could bend the shoe almost in half with my hand. And I'd look at the shape of the sole that it would allow their toes to fan out (like a birkinstock shoe, or crocs for example allow for my own toes). If it was thicker or stiffer, it was earmarked as 'the shoe' for hiking, visiting farms, etc where you'd want harder and heavier shoe protection. I personally don't always pay attention to arch support and haven't read up on when/how it makes a difference even for myself (and I possibly should) so can't give you my recommendations about that.