All too often, "stuff" (AKA, "user input") is NOT "secure" for values of "secure" which eq "safe to allow."

And, by "spending a lot of time untainting" I'm guessing that you mean "writing code" as opposed to "spending" a lot of CPU time.

If so, it's a one time cost that will be repaid the first time untainting saves your bacon (AKA, "site, reputation, or fortune").

I am very happy with the answers, but I will offer a clarification just in case this produces a different answer - or at least a deeper answer. I am not casting doubt on the -T argument in perl. I absolutely see the point of that. I'll explain the example that is bugging me at the moment. In the form element I need to post back a $my_cgi->start_form() into the HTML::Template variable <TMPL_VAR NAME="form">. In HTML::Template I am using that module's force_untaint option and it is complaining about taint. Given that when the submit button is pressed, the arguments passed to the CGI script will be checked for taint, why do I need to check the HTML shown to the user for taint?

why do I need to check the HTML shown to the user for taint?
Same reason, security. From the docs:
force_untaint - if set to 1 the module will not allow you to set unescaped parameters with tainted values. If set to 2 you will have to untaint all parameters, including ones with the escape attribute. This option makes sure you untaint everything so you don't accidentally introduce e.g. cross-site-scripting (CSS) vulnerabilities. Requires taint mode. Defaults to 0.