A proper riding boot is not for a "look" it is for safety. You want a boot with a heel and preferably a tread, one that is designed to not allow a foot to slip through a stirrup. But a big heavy boot or shoe may be too wide for a stirrup or leave little room and a foot could get caught or trapped in a stirrup, something that no one ever wants to happen.
I was told all that too, and I haven't worn riding boots while riding in over 35 (close to 40) years now. Never had the first problem in all that time. The protection part would be true except that my leggings actually do a better job for my legs and the shoes are WAY more comfortable than any riding boot. There is plenty of foot gear (other than riding boots) that work fine with a stirrup.
Boots are like a lot of things that people have clung to from the past (although the military started moving away from in the late 1800's when they started using more leggings with ankle type boots, but boots where still around....especially with the officers...."traditions" die hard). Lets face it, they still have swords
, and while you can still kill someone with one you'd be hard pressed to argue that it's a needed weapon for the military. Mounted troops rode more than enough to discover if there was a problem or safety issue with walking boots and leggings.
"Boots" are really all about clinging to a style or a tradition. Not that there is anything wrong with liking a style/look or wanting to follow a tradition. Doesn't mean it's needed though, when there are things that do the job just as well (or in my experience, better).
But if you find a riding boot that protects my legs better than my Austrailian WW I leggings (US made a very similar and equally good leggings too, but later I had better access to the Austrailian ones) and feel as comfortable walking 10 miles in as my foot gear then do let me know
And unless things have changed dramatically since I was taught to ride (unlikely even after 45 years) what protection do you need when you're riding around an arena that any appropriate pair of foot gear doesn't provide?
I wore boots and liked the look (especially on the lady who taught me to ride, along with her tight riding pants
), but when I started really working on horseback, riding long distances along with spending time working dismounted, etc... riding boots (even "cowboy boots") did not measure up to good shoes or walking boots and military leggings. One of the many things I quickly learned from some of my older family members who never wore any kind of riding boot.
It depends on what you plan to do. If you're going to always do arena riding and never ride out very far so that walking very far would never be a possibility then boots might work ok.
OP you can probably still find some new, surplus riding boots with military surplus sales under some foreign military surplus. I'm sure there are online places that sell them. E.g. The old Soviet Union officers were still wearing riding boots (complete with the slightly higher front on top) right up until the end so there should be loads of them still available. An uncle of mine picked up a pair in the 90's when he needed some riding boots for an event that required the boot (for historical look). I think my oldest son has them now (he loves the look, but doesn't ride