Yep. When we started our support was done through individual emails or a general support email (not tied to a ticketing system). That was fine when we were a 5 person company with 3 big customers.

As we scaled, we had to transition to a ticketing system, for the reasons you mentioned.

Slack definitely feels backwards in some ways especially if you use it as a channel for dealing with customer requests, especially if multiple people at customer site are part of the slack group.