Your understanding of the tonic chord seems just fine.
Your real question is about locrian mode an whether a diminished chord can be a tonic.
I think you should make a distinction between what are musical conventions and some notion of absolute, objective musical qualities.
There is a very long traditional and some acoustical support of the sense of stability in root position major/minor triads. The perfect fifth is what really gives the sense of stability to these chords and therefore the lack of stability in diminished or augmented triads. Another way to think of the "instability" is augmented triads and (fully diminished seventh) diminished chords do not have one single root position inversion. That particular aspect of augmented/diminished chords is often called symmetry, it gives them a certain ambiguous quality, and that ambiguity could be thought of as the "instability."
Another very old tradition is starting and ending a work on the same chord, the tonic chord. There isn't any acoustical rationale for this, but you can make various comparisons to other arts: an architectural arch, the hero returning home in narrative plot, etc.
Neither of those two traditions is a physical law of the universe. As much as people want to invoke acoustics and the overtone series as a rationale for why root position (major only) chords would be perceived as stable these traditions are cultural choices. Being conventions a musician (that an artist not a scientist) can conform to the conventions or buck them intentionally however they see fit.
I think a nice composition to use as an example is Chopin's Mazurka, Op. 17 No. 4, in
A minor. Neither the start nor ending use an
A minor chord, nor even a root position major/minor chord. The first clear confirmation of
A minor isn't until around the 20th measure, and just before the final phrase there is a clear
A minor statement. Incidentally, the very first chord is in ascending order
A B F, which you could say is a half diminished chord in fourth inversion, that would superficially be a tonic chord for
B locrian. Sonically, you can hear the diminished quality of the chord, but I don't really think it's a locrian tonic, I'm just pointing out the coincidence.
We can play around with metaphors and say the ambiguous opening/ending phrases are introduction/coda representing some emotional or nostalgic turning away while the
A minor statements are affirmations, some kind of "home." You could turn it around, the ambiguous opening/closing is some kind of tragic "home" and
A minor, and the whole middle section, is some escape fantasy, etc. etc. You can go on and say anything you like about it metaphorically. In technical musical terms Chopin started and ended with an ambiguous phrase using inverted chords of the sixth and placed statements around a tonic
A minor internally using the harmonic conventions of tonic/dominant harmony. Nowhere in the music did anyone or anything "go home."
What do you mean by the tonic chord feels as 'home'?
If you don't know music theory terms, explaining tonic with a technical explanation about leading tone, perfect fifth, root position, etc. won't make sense. But, a metaphor that fits a lot of music listening experience will. We could play something simple like Handel's famous sarabande in
D minor, point out the starting on a
D minor chord, the movement to other chords, and then final return to
D minor, have all agree this feels like the music is coming to a conclusion, metaphorically call in returning to "home", and then say that "home" feeling is what make the
D minor chord the tonic. The technical fact that those "home" tonic
D minor chords are all directly connected to dominant chords is skipped... unless the person is starting to learn music theory. In that case the tonic/dominant relationship is exactly what you point out and explain is actually the way the tonic is defined in music.
Can locrian mode, or a diminished chord be a tonic? Well, by long established historic conventions: no. It would literally be reserving the harmonic roles. A diminished chord normally acts as a dominant or the
iio in minor is a subdominant.
If we broaden the meaning of tonic to just mean some "main", "central", "focus", etc. tone or chord - sort of the "home" idea - but rather than being defined harmonically with tonic/dominant chords, it will probably be achieved rhythmically, you could have a so-called locrian tonic. Adam Neely has a good video showing several musicians playing in locrian mode. To the extent that the stuff is in locrian mode we have a locrian center, a tonic.