Changes
if the noprint and inline-template classes need to be preserved, according to the docs, then why not enforcing in the code rather than asking people to do it (and relying on them reading the docs attentively enough not to miss that)?
{{#switch:{{{subst|¬}}}
|¬={{category handler
|template=[[Category:Templates needing substitution checking]]
|nocat={{{nocat|<noinclude>true</noinclude>}}}
}}
|SUBST=[[Category:Pages with incorrectly substituted templates]]
}}{{Category handler
|main={{Fix/category
|cat-date={{{cat-date|}}}
|cat={{{cat|}}}
|cat-date2={{{cat-date2|}}}
|cat2={{{cat2|}}}
|cat-date3={{{cat-date3|}}}
|cat3={{{cat3|}}}
|date={{{date|}}}
}}
|template={{#if:{{{name|}}}|{{#ifeq:{{{name}}}|{{ROOTPAGENAME}}||{{#if:{{{date|}}}||[[Category:Templates including undated clean-up tags]]}}}}}}
|subpage=no
}}{{#if:{{{text|}}}
|<sup class="noprint Inline-Template {{{class|}}}" style="white-space:nowrap;">[<i>{{#if:{{{pre-text|}}}
|{{{pre-text}}} 
}}[[{{{link|Wikipedia:Cleanup}}}|<span title="{{{title|{{{link|Wikipedia:Cleanup}}}}}}{{#if:{{{date|}}}|<nowiki/> ({{{date}}})}}">{{{text|}}}</span>]]{{#if:{{{post-text|}}}
| {{{post-text}}}
}}</i>]</sup>|{{{special|}}}
}}<noinclude>
{{Documentation}}
<!-- Add cats and interwikis to the /doc subpage, not here! -->
</noinclude>
|¬={{category handler
|template=[[Category:Templates needing substitution checking]]
|nocat={{{nocat|<noinclude>true</noinclude>}}}
}}
|SUBST=[[Category:Pages with incorrectly substituted templates]]
}}{{Category handler
|main={{Fix/category
|cat-date={{{cat-date|}}}
|cat={{{cat|}}}
|cat-date2={{{cat-date2|}}}
|cat2={{{cat2|}}}
|cat-date3={{{cat-date3|}}}
|cat3={{{cat3|}}}
|date={{{date|}}}
}}
|template={{#if:{{{name|}}}|{{#ifeq:{{{name}}}|{{ROOTPAGENAME}}||{{#if:{{{date|}}}||[[Category:Templates including undated clean-up tags]]}}}}}}
|subpage=no
}}{{#if:{{{text|}}}
|<sup class="noprint Inline-Template {{{class|}}}" style="white-space:nowrap;">[<i>{{#if:{{{pre-text|}}}
|{{{pre-text}}} 
}}[[{{{link|Wikipedia:Cleanup}}}|<span title="{{{title|{{{link|Wikipedia:Cleanup}}}}}}{{#if:{{{date|}}}|<nowiki/> ({{{date}}})}}">{{{text|}}}</span>]]{{#if:{{{post-text|}}}
| {{{post-text}}}
}}</i>]</sup>|{{{special|}}}
}}<noinclude>
{{Documentation}}
<!-- Add cats and interwikis to the /doc subpage, not here! -->
</noinclude>