A custom indexer for ke_search would be very nice.
An indexer that works for all mask elements without or with little effort for the integrator.
https://www.typo3-macher.de/en/facettierte-suche-ke-search/dokumentation/ein-eigener-indexer/

Actually, that wouldn't require an own indexer, but a hook, as described for DCE on

https://www.typo3-macher.de/en/facettierte-suche-ke-search/dokumentation/konfiguration-des-indexers/indexer-fuer-seiten/

Then the hook like:
https://bitbucket.org/ArminVieweg/dce/src/72e9dcc3d2c1da0067ff47c844bdc0c02bcef598/Classes/Hooks/KeSearchHook.php?at=develop&amp%25253Bfileviewer=file-view-default&fileviewer=file-view-default

to render the mask item and return it instead of bodytext.

Also see (custom indexer) https://github.com/BenjaminBeck/bdm_kesearchindexer_flux/tree/master/Classes/Helper

Of course, they could be passed through their Frontend templates in the "Content" dir.
But a faster solution would be to create a third template directory "Search", alongside "Backend" and "Content". There, simplified versions of each CE could be stored that just contain the data we really want to index.