> Do folks get 3am phone calls to open up a server and dig through restarts?

No, back then it would be a 3am pager beep; triggered by Smalltalk resumable exception, possibly when someone was on-call (in a bar).

> … nice to log in to a server, tweak a piece of code, and let it continue on?

Critical not "nice".

Trade reconciliation done upstream on mainframes took many hours (not enough time to do over) and that upstream processing was sometimes broken when it was changed, and then those errors were caught and mitigated by downstream software — because there we could "tweak a piece of code, and let it continue on".