No, it should not. First, thinking of the results table as the same table as one of the tables that participates in a query is defeating the power of queries and the results tables they produce. Second, selection is an ad hoc, casual, interactive tool while SELECT is a gateway to the full power of SQL. [...] If you are leveraging SELECT then use the power it has [...].
The right way to do what you want is to keep a snippet of SQL lying about that you can copy/paste into your queries to create a drawing on the fly from the results. You can then drop that drawing, which shows the resultant geometry that your query picks out/creates, into a map as a layer. Clever symbology, such as larger point symbols in a contrasting colors, can do an even better job than Selection red of highlighting. You can also create drawings dynamically from queries that involve selection. See Example: Create a Drawing from a Query
Use The Force, Luke.
When I want to find a parcel owned by a certain person, a query seems to be the only way to sort through and find it.
No, it is not the only way. I am puzzled you wrote that, given how immediately afterward you described workflow using Filter, and not a query. :-) You could also use the Select panel. You can see the interactivity between a table, a drawing, and the Select panel in the Example: Combining Selections using the Select Panel topic.
If I wanted to find a parcel owned by a certain person, I'd use Ctrl-F for Find or the Select panel. To get more, right-click into the cell that gives the name and use Filter. It's instantaneous. You can then select and see in the map, etc.
What I find myself wanting is to right-click on the field name and finding a Search or Filter box as an option.
If you click on a column head, Ctrl-F automatically by default launches with that field as the target for the Find. It would be interesting to add a checkbox captioned "Filter" next to Whole world only and Ignore case.
[Edited to remove the simile, which sounds too strong in English compared to the use in the original.]