The single biggest child site issue that you can end up dealing with is why is the site email not being sent. You could use an SMTP plugin and then use SMTP creds to connect. But using a transactional email provider makes it easier in knowing that your child site email will be delivered correctly.
The delivery of site email can be a pain to deal with on child sites. If a site is using WooCommerce or a form plugin like Gravity Forms, you want to ensure that form notifications and customer order notifications are being sent out to customers. The easiest way to resolve site email deliverability issues is to use a transactional email provider. The company behind Ninja Forms recently launched a new monthly paid service called SendWP.
SendWP does not require a lot of setup in contrast to SendGrid or SparkPost. An account on SendWP can be created by installing the plugin on the child site, then follow the steps to connect and signup for an account. SendWP offers a 14-day trial, but with credit card details having to be entered before the trial can be used.
SendWP offers a very simple level of pricing which is $9 per site, with no limits on the number of sites email per month.
If you are looking for a simple option for being able to reliably send site email, SendWP is worth looking at.