Everyone has numerous reasons NOT to use an issue tracker. Few reasons that the old style management people say are:
We already use Excel or Google spreadsheets to track the issues. We put individual issues in each row of the excel sheet and the person who is responsible for it.
You could try sending out excel sheets through email and ask everyone to update the sheet end of date, but who will handle the conflicts? Or you could use Google sheets to allow everyone to edit it together. Even then, conflicts are possible.