I am new to the game. Been only playing for a month. One thing I learned about the game, though, is that some champs need to not be fed, or else they will wreck my team. Now gold will be easily available and those champions will easily be able to get their items to be able to wreck. So we will see Xins and Akalis and Veigars and etc running around and destroying people in 2 seconds.

So now that people can easily get their end game items, do you think certain champions will "shine" and cause more outcry on being very powerful?

except those resources are given to everyone, and veigars gonna be useless on dominion without a farmfest

You are new to the game so you might have problems fighting with some champions, especially when they are fed. Truth is while some champions are slightly stronger then others there is not one instawin unstopable killer machine that can kill anyone whith his equipment filled with items. Preremake Trynda might have been a problem but it was taken care of.
Akali actually falls of late game when people build a bit magic defense and her burst is no longer instakill. Xin can either build tanky and then doesn't deal so much damage or is super squishy and killable in one CC duration. Also he is getting nerfed. As for Veigar (and Nasus...) he will be trash tier in Dominion as his damage comes from farming and you simply won't have time for that.

Veigar still is great pick. His W has great ap ratio, E is one of strongest stuns with great utility, R being easy mode, easy kill ulti and Q is still good spamable skill even without farm. And you forget that bonus ap from kills is only bonus and he can still farm champions... Especially when Domion is focus on killing, when Veigar gets 10 kills with 5 lvl of Q, he gets additional 50 ap for free.