It logically does not make sense to add a taxonomy custom search filter to a taxonomy archive page because there is already an effective filter in place for the current taxonomy term for which this archive is.
For example, if you have a city taxonomy and you are viewing the archive for Madrid at site.com/city/madrid/ which shows posts that have the term Madrid, it does not make sense to include a filter on that page where users can search for posts about Paris. (But it might make sense on such a page to include a filter for a custom field to only show posts which are 'featured' which is why it is possible to create custom searches on archive pages.)
For something like that you should create a static page and include a View where the user can choose the term in a filter to show such posts, and can update the filter to change the results.
No, because the results at the taxonomy archive URL are generated by WordPress according to the term in the URL. Any filters (e.g. custom field filters) which Views then applies on that page narrow-down the initial set of results. Clearly, you can't narrow down the city/madrid results to city/paris, you need a completely different set of results (which are generated at the city/paris URL).
Hence filtering by the taxonomy needs to be done with a View on a static page, not on the archive itself.
