You're completely missing the point that Byzantine's UA can be effectively denied forever which can happen easily. No other civs' UA can be rendered useless unless you choose not to use at all during the whole game. Spain don't have natural wonders bias but so what, they always get the 2X output from NW and they get at least 100G when discovering one, whether you find and occupy one during classical or modern age. UA which are purely war focused such as China or Mongol may seem useless for a peaceful game, but they can be activated as soon as you want to start a war, whether it's ancient or industrial age.
Is luck involved for them? Sure, but it doesn't really matter, because at worst their UA becomes only dormant and can be used SOMEDAY. And their UUs can actually help them get a better result from the the UA. You know, synergy.
For Byzantine if you don't pursue a religion right from the beginning, you can be blockaded forever from ever activating your UA. And getting a religion fast requires a lot of luck. If your luck doesn't help you, your UA is not dormant, but DEAD. Their UU doesn't provide any synergy for activating their UA whatsoever as well, unless you consider wiping out neighbours with cataphract rush to prevent them from creating religions synergy. But then you won't be ever able to get a religion up and running in a timely fashion again.
Also, "requiring luck is a good gameplay" is not an excuse for bad game balancing. Currently Byzantine's probability at getting a religion is the same as every other civs except for Celt, Maya and Ethiopia. Which means if we reduce the luck involved variables such as terrain and ruins to a minimum (but not removed) and let all the players pursue a similar route of development including religion development, there's a good chance that Byzantine may never be able to get a religion running (or only getting a bad one), therefore having a dead UA. Now consider that all other civs have no such problem as they can always put their UA in use if they choose to. That means in a game of balanced luck, Byzantine being the only civ that may have no UA at all from the beginning till the end, is statistically weaker than every other civ.
This is not even a "bad gameplay" or "bad luck" thing. It's simply bad game balance. Byzantine's UA is statistically weaker than other civs. Byzantine is currently the only civ that can become BLANK post classical age because even their UU get obsoleted fast and their special skills don't last after upgrading. Sure! You may have fun and find it challenging playing as a handicapped civ. But it is a pure statistical fact that Byzantine is weaker than other civs and it SHOULD be addressed if Firaxis and players value game balance at all.