FFXIV had a great solution, which was to tie a daily/weekly challenge to giving commendations to other players. It awarded a small amount of Gil for completion.
Something similar in Overwatch couldn't hurt.
That wouldn't work as well. The differences in Overwatch economy (read: there isn't one) and FFXIV or WoW are too numerous to count.
For an example, and I highly suspect that this is their train of thought -- giving you currency, even 1 per day, can dissuade you from buying your sprayboxes because everything is so "Cheap." In fact, the currency is deflated enough that each singular currency point is worth much more that it looks like on the tin.
If they were going to go that route, they might want to do 5 or 10 per day, but again, why would they? Purchasing boxes is what they designed the system around, and the horse keeps coughing up money when you kick it. We're the horse. They don't want us to work gradually toward getting something, they want us to buy loot boxes.
Contrast this with FFXIV, which uses gil(now, anyway) for teleportation, for consumables, for repairs, and all sorts of other things under the sun. It has currency sinks. Overwatch has currency sinks in the vein of ...sprays. But let's be honest, nobody actually WANTS sprays when it precludes you from getting other things, like skins, or highlight intros, or emotes, or even voice lines. The sprays and player icons serve as a buffer to keep you playing and keep you buying boxes for more chances at that sweet, sweet legendary you have your eyes on.
That's why Jim Fucking Sterling, Son dislikes microtransactions -- it's not that they
exist, it's that the game is
always built around microtransactions, and not the other way around.