Is there any reason why you can't see the enemy team's borders?

They removed this some time ago, around the same time they removed everyone's ping but your own. If I recall correctly, this was an effort to prevent trolling, negative attitudes, etc. due to anxiety about mismatches.

Think of it this way: You are Gold II, and playing normal queue. The enemy sees that you are the only gold+ player on your team. Since the enemy now knows that you are the most dangerous enemy, they will either A: Gank you non-stop, thus ruining the game for you. Or B: Avoid you completely, ruining the game for your lane opponent. Neither outcome is very fun, and so Rito simply removed the enemies ability to see your rank.

It's easy to look up though. If you got to lolnexus or kassad.in you can see the tiers of everyone in the game easily. And the border does not even really represent your tier. It's a bad approximation from some time ago and you might be somewhere very different now. So IMO the borders are pretty much useless since they're mostly just misleading noobies into thinking people are in tiers that they aren't. I wish we couldn't even see any of them.

lolskill is another, but I like that it's not freely available information. I support the lack of borders, makes things fun. No one will psych themselves out going again a Gold +

They removed it awhile back probably trying to hold people's hands, I don't know.

You can just check any of a multitude of sites if you actually want to know though, so it's pointless