I have terribly high insteps. Little A has the same problem. Both our feet look like this, but much less knobby and Microsoft Paint-y:
As you can tell from this fantastic painting job, we're also both very narrow-footed, which is a pain because you have to get bigger shoes to accommodate the height, which means that your foot slides around back and forth. The old adage is that a high instep is a sign of aristocracy (higher the instep, more elite the bloodline) - all it means these days is that it's a giant pain in the crack to buy shoes.
We didn't buy A shoes until she was walking - from everything I read (and I read a LOT), it said that you should wait to put them into shoes until after they were used to the feel of the floor. Also, it was cheaper. Win-win. Her first pair of shoes were some "Tommy Tickle" ones I got off of Zulily - they were soft-soled so that she could still feel the floor, but sort of eased her into shoes (which she was fighting by throwing themwhenever we tried to put them on her). They worked well, and accommodated her high instep/tall foot well. It was also a gentle way to make the transition.
We had a pair of little Keds next to make the transition to hard soles, but she refused to wear them - so we next bought some squeaky shoes. Not squeaky as in "oh, they just need to be broken in" - no, these shoes had some device in the toes that squeaked like a dog toy every time she took a step. It was cute for, oh, say, the first hour. Then I wanted to throw them away - as did our amazing nanny. Unfortunately, A loved them, and was bummed when we did transition her to the Keds. The Keds worked okay, but her little foot was fairly crammed into there pretty tight, and I hated seeing the little marks they left on the top of her foot.
I looked at Target, Payless, Penney's. Nothing really has much in the way of options for infant/toddler shoes, so you're sort of left looking online. I looked on Amazon, and the reviews showed mostly shoes that weren't going to be tall enough. Seriously, where do people buy toddler shoes, and where did they do it before the internet?
So, I made the next step up. Stride Rite. I was a little nervous about this because their shoes are a bit pricey when you consider that toddlers grow shoe sizes every few months, but we really had very few other options.
We went with the Stride Rite brand of tennis shoe. This isn't the exact one, as it was an older style, but it's pretty similar (LINK), ran about $35:
It's probably hard to tell when there is no point-of-comparison, but this is actually pretty tall. I don't know that it had a whole ton of arch support, but it at least didn't gouge into her tiny little feet when she wore them. They held up really, really well, and they had really good traction. They were still a little wide for her narrow feet, but better than the Keds had been with the wide, flat bottoms.
Their sandal options weren't quite as great, most of them were a little low and cut into her foot, so we've changed to Adidas sandals since. Flip-flops don't really work all that great on a climbing toddler, so we only use those for the pool or hot tub.
This post is relevant to maybe 10% of the parent population, as I think wide feet are a much bigger issue with littles, but hopefully it will be useful to someone. I did just order a pair of New Balance tennis shoes, I'll see how those go. There seriously needs to be some sort of "rent-a-shoe" thing online where they'll mail you shoes and a return box, and you get the shoes for 48 hours to try on your child, it's impossible to eyeball shoes on the internet.
Value: $35. A little more than I want to spend for multiple pairs of shoes every few months, but it's literally the only option I've found.
Child entertainment level: N/A
Practicality: If your toddler has high arches/insteps, this seems to be the best option available.