Updated again May 2 2019 becaise @zephyr1 linked to this post and iy is not 100% accurate.
TL;DR - current data indicates 18 months to collect 15000 emblems (enough to max 10 5* heroes if averages hold). Emblem rewards from raid tourney are mediocre at best and seasonal events (spring, summer, autumn, and winter) do not have emblem rewards for some reason.
Personal speculation thinks that SG will continue to add and adjust emblem rewards to bring the 18 month mark closer to 12 months but that is based on literally nothing except my “good feeling”.
UPDATED MATH TO REFLECT CURRENT DATA AND ADJUSTED FOR CLASS QUESTS
I have received 125 (not counting the 250 emblems given as a gift from the devs) emblems in relatively 7 days. I have killed killed a 12* titan every day (1 rare), pushed chests as often as possible with only 1 elemental chest (speed up the timer), opened 2 titan chests, and opened 1 war chest. Without analyzing the amounts of emblems from where etc (this post is ONLY to determine if the odds are reasonable) - i think it is fair to say that this method allows for as many emblem drops as possible. That being said - With this math of 18 ish emblems per day (whcih includes the 72 per week from the quests) - needing 15,000 emblems to max 10 5* heroes (1 from each class @1500 each); that means 125 emblems a week (give or take). 125 x52= 6500 emblems a year. It will take 15000Ă·= 2.3 years to max a full set of heroes (10 - 1 from each class). To that I am optimistic.
The devs have responded saying many things but one of the most relevant to this topic is that “there are more sources of emblems yet to be released”
My personal opinion is that the emblem drop rate is low but not unreasonable however, it appears that there will be more sources available so it’s ok with me.
This data is from a single character not multiple
This post is from stormy lady (for those of you familiar with the joke on line)
Cheers!