Pieces tend to modulate--or tonicize--often. Not all key changes are associated with key signature changes. The key of a piece, or more often a section, may be ambiguous. Combine these three reasons and an additional marking for the tonic in a key signature becomes clutter, useless, or even actively harmful.
Baroque music modulates fairly often. Fugues often put their first answer in the dominant key of the home key, yet they often do not change key signatures at all. Other contrapuntal music such as minuets and preludes also tend to change keys without changing key signatures. Note that Baroque music often contains the overall key of the piece in its name, yet those do change keys.
Classical music also modulates fairly often. The convention for sonata-allegros of the time is often to either refuse to change the key signature at the development or to strip the key signature at the development for chromatic enough development sections (e.g. the printings of the 1st movement of Beethoven's Appassionata Sonata I'm familiar with). Yes, this is the convention of the part of the sonata-allegro that modulates the most. Another convention is to not change the key signature of the sonata-allegro during the entire exposition, despite invariably changing keys halfway.
The key of pop music is sometimes ambiguous--is that song in a major key or its relative minor? I personally have encountered that problem when trying to determine the keys of Kelly Clarkson's "Behind These Hazel Eyes" and Avril Lavigne's "When You're Gone": both pieces have (at least seemingly) major-key choruses, yet they end the choruses with chords that match the tonic of the relative minor.
I'll pause here to note that, almost by definition, tonicizations are pretty much never associated with key signature changes. This is because of their temporary nature.
And, sometimes, it's ambiguous whether a phrase involves a tonicization or an outright modulation. Is the very early shift to E flat major music in Jon Schmidt's "Road Trip" a full modulation, or is it a tonicization because the music weaves out of and back into C major in a mere 4 bars? At any rate, the sheet music of Road Trip does not change key signatures there (at Bar 5).
Given these examples, it should be apparent why an additional indicator for the tonic at a key signature is often counterproductive.