Would be nice, yes.
But how often do you really perform individual searches with the same keyword in several content types?
I honestly can't remember a single time I did this.
The interface isn't ideal anyway - you can search all content types at once on one tab or one content type at a time on other tabs.
It would be better if this was just one search form that allowed to search all or just selected content types with specific options for thoses thyes.
Internally, this would have to perform N searches if N content types are selected with specific options and merge all those results together for final output.