Developers will write estimates when it becomes easy and relevant to do so. They will not estimate just because you email them. In addition, emailing developers as individuals will be likely to result in individual estimates: made in isolation, without consulting the group, and with all the resulting anti-patterns which come from rewarding / punishing individuals.
It's also likely to get devs' backs up. At best, they'll simply filter the emails out. At worst, this will result in conversations like, "Oh, sorry, I missed the meeting invite - too busy dealing with the estimate emails."
This will make PMs / SMs happy only in the very short term, until they realize the side-effects of the feature and turn it off. Please, please don't do this.
If you want to help developers estimate, focus on letting the developers know - through broadcast, rather than through push - that a particular task needs to be estimated. This could be done with a normal card wall and a small piece of text or an icon (I'm not seeing such a card wall in your product, but that's the right place for this IMO). It needs to be optional as some teams only estimate when they pick up the story or (in the case of Kanban, for instance) use recorded data for estimation purposes instead of guessing.
Also focus on making it as easy as possible for developers to add estimates, or to read them automatically from whatever tracking tool they're using. That will help more than any number of emails. Wherever possible, assume that people want to do useful things and put your energy and creativity into making it easier for them to do so, rather than forcing them to do so through other features.