I see no merit to an argument about operating costs if, by that, ongoing costs is meant. If it's 'Operating Costs' in the broader business terminology sense then, yes, there would be a small initial development cost.
You can see that each comment displays three bits of information: Who, When and What. There's a fourth - Where - so it can be tied to the entry the comment was made on. Every comment has a unique entry in this site's 'Comments' database table containing those four bits of info.
Two ways come to mind to achieve what's been requested: (1) Search the 'Comments' table each time the list of comments made by a particular user is required and output a list of those comments. (2) Create a new field for each user holding the unique ref numbers of every comment they've made, then add each new comment ref to that as it's made.
(1) is extremely easy to implement and should require virtually no ongoing maintenance. Given the high number of comments on the site though, it would probably be relatively slow and resource heavy.
(2) is a bit harder to implement but once the structure is set up it should, again, require virtually no ongoing maintenance. It would be much faster than (1) with minimal processing resource needs.
Nearly all costs would be 'one off', and mostly associated with making the result look acceptable visually.