Yea they really want you to buy the new champs that come out. Couple different sources put out a figure of close to 40 hours of game time, not down time between games, just in game time to earn 10,000 gold. That's winning around 120~ games to get a 10,000 gold champ, the new ones come out I think start at 20,000 or 15,000.
if you do your daily quests you can get at the very least 500 gold a day. thats only 30 games, doing the bare minimum. and each quest takes about 3 games, so you are looking at getting 15000 gold every 2 weeks or so with like 1 hour a day investment. thats faster than the new heroes come out