A lot of recent tools like Intercom and GetVero and Customer.io can help make this even smarter by emailing about specific abandoned tasks, different emails to those who aren't engaged at all, or not emailing someone who is fully engaged.
Just as a data point, let me tell you how my mind works because I'm the person your raw numbers won't tell you about:
Just getting the emails is likely to annoy me unless it's really, really earth-shatteringly useful and I've yet to ever see an example of this. I'll likely open the email and give it 1-2 seconds of scanning time to make sure I'm not missing out and to find the unsubscribe link; if I can't find that, I'm hitting the spam button which (for a service like gmail) will in some small way affect deliverability for other users.
Nagging me about abandoned tasks is really irritating and it would teach me that using the service "improperly" is likely to lead to my inbox filling up with no-shit-sherlock emails, and would make me want to avoid using the service at all just to avoid this fate. If I abandoned a task, I did it deliberately and really don't want to be punished with email.
Begging me to come back because I haven't logged in in x days is likely to piss me off too. If I haven't used a service in x days it's because it wasn't useful to me and an email isn't going to magic it into the opposite. If anything, you might actually be offering me social proof from (my past self, not others) that the service isn't useful!
When I'm evaluating an app during the free trial I've likely made up my mind within the first 30 minutes, if that. I'm looking to see if it's usable, useful, and beautiful, and if I can't determine that from experiencing the app, email isn't going to save the day.
If I abandon it within 24 hours I'm almost certainly never coming back, except to cancel the trial if I've already entered my credit card details.
If there's a high abandonment rate, emailing people after a trial is over to ask them what pissed them off (giving them the option to submit anonymous comments) is more likely to lead to useful information that will increase retention by improving the quality of the app. But nobody is ever going to say they abandoned a service because they didn't get enough email!
Email has never persuaded me to use an app I've abandoned, but I begrudgingly accept my fate of more email whenever I sign up for a free trial as non-monetary price I must pay to experience the app. If irritation is a currency, apparently I'm broke.
For anyone with experience in this, does it just come down to weighing the benefit of gaining a customer against the risk of losing two?
There was someone who's articles and videos I'd share on reddit because they contain (and still do!) really, really great content. The trouble is, they're now wrapped up in overly-aggressive marketing tactics. The videos now have a YouTube ad and a 15 second intro lead-in that reminds me of the THX intro clip [1]. This is followed by an advertisement for other products, followed by the actual content, followed by the spammiest looking "click subscribe!" clip. If you visit his website for the first time, you're now immediately greeted with a popup asking to subscribe to their email list. Again, really great content wrapped up in unempathetic marketing tactics. Last time I shared something he'd created on a targeted subreddit, everyone immediately bitched it was spam and it was downvoted; they missed the content because of yucky marketing.
Every time I'd post a link, pre-unempathetic marketing, it would (apparently) net him a lot of traffic and reach a previously untapped audience. (I'd get a thank-you email for the huge spike in traffic!) Social media traffic is harder to convert but can be done quite effectively when done properly. What this person can't measure is my current unwillingness to continue to share his best content because of these overly aggressive, unempathetic tactics. I put up with them and still consume his content because I know it's good and it appeals to my interests, but it seems to make newbies bounce very quickly.
There are marketing tactics that "work" and will result in a positive bump in metrics but have an ick-factor to them and hidden cost. Same deal with on-boarding emails, nagging emails, jQuery popups begging for an email address, etc. They have tangible results and appear to be working, but the undetectable damage is still present.
My general rule of thumb is that if you wouldn't want someone to subject you to the tactic, don't subject others.
Many people here will also tell you that $100 a month is an outrageous price for a service that saves time for software engineers. It is true that they feel that way, but it's a mathematically false statement.
At Klaviyo (I'm one of the co-founders, so note bias), we've helped many web apps and ecommerce sites setup full email strategies - and we definitely find that some emails don't work. You've got to test different emails and strategies, see what works - and then ideally optimize and personalize what (or even whether) you are sending based on individuals' actions.
I've observed that some less-savvy people don't know how to unsubscribe from emails, or fear doing so will "upset someone" and so grin and bear an otherwise annoying deluge of email they never react to.
It doesn't feel great to be told you're unimportant, and no company owner will say that to their own customer, but really — you and I are not that important. I do not expect McDonald's to abolish all their meat products because they offend me as a vegetarian — the rest of their customers manifestly do not share that opinion, so it would be a dumb choice if they killed the Big Mac. Similarly, it is not in a company's best interests to terminate an objectively successful email campaign just because some random guy got pissed off but was unwilling to click Unsubscribe. Successful companies lose customers all the time for all kinds of reasons — they would never get anything done if they tried to personally appeal to every single person on earth.
Again, McDonald's pisses off millions of vegetarians every single day. Would you say on that basis that they should go meatless? Should churches close to avoid pissing off militant atheists?
The point is not that you should be callous about offending people. Obviously it is better for all involved to make people happy, and that should always be your goal. But the point is that one or two guys saying "I'm so angry!" on an Internet forum does not mean you've failed. No matter what you do, even if it's pure charity work, you'll eventually find someone who gets upset about it. All you can do is apologize and offer to unsubscribe them — it's not rational to throw your business away on that basis.