Problems would happen when the new person tried to log in to the account. Since the login was from an unrecognized device and an unrecognized IP address, security was tightened. Even after inputting the correct password and entering the right backup email, it was mandatory to enter an SMS message from the phone number tied to the account, even after various troubleshooting and attempted workarounds. That meant getting ahold of the previous executive, who may be busy or changed their number.
You could argue that Gmails weren't meant to be used this way, which is fair; the goal of this comment is just to provide additional evidence that the description provided by the parent comment is true. (In the end, we went for a low-cost, reliable email service to fix the issue in the long-term. We also found that registered non-profits are eligible for free Google Workspace or Microsoft Outlook email plans subject to certain eligibility conditions, though we did not have a need of becoming an officially registered non-profit at the time.)