I am not sure what the "all tickets" menu item is configured to do. There is no such thing in ATS. There's either a menu item to show the categories or a menu item to show the tickets inside a category. I will assume it's the latter.
The important factor in the response time is the number of tickets you are displaying at once, i.e. Joomla's default list limit. With the default limit of 20 displaying one page of 20 tickets takes 470 msec on a mid-spec server. If you are trying to display all 27,000 tickets in one insanely long page I would expect PHP to crash due to lack of memory. If you have a really big limit (e.g. 500) you will have a really long delay before anything is displayed.
Remember that in order to display the information for a single ticket we actually have to load both the ticket and its replies. Otherwise we would not know who was the last person to reply to the ticket. Moreover, we have to load the user information for every unique user in the generated page. Otherwise you'd see, for example, that the ticket is created by user 123 and last replied to by user 456 instead of created by user Paul. and last replied to by user Nicholas. These are additional queries which do take up time and memory to execute.
The only thing you can do is limit the amount of information displayed per page. Go to System, Global Configuration, Site Settings and set Default List Limit to 20.
Nicholas K. Dionysopoulos
Lead Developer and Director