I believe that tonal harmony is a technique that has been used in a wide variety of musical styles and the assumption that it was exhausted was short-sighted. The kind of tonal harmony that was chosen by Classical and Romantic composers came to an end because those periods came to an end. New kinds of musical expression came to the fore. Let me chose an example to show what I mean.
The harmonic sequence was very important from the late 17th to mid 19th centuries. There were various kinds: descending fifth, ascending fifth, ascending 5-6 and falling thirds. All these sequences used pairs of chords. As time went on they were ornamented in various ways with added sevenths, applied dominants, augmented sixth chords and chromatic voice-leading, but the basic principle was the same: pairs of chords. Sequences were hugely popular because they gave a strong sense of harmonic motion, but still strengthened the harmonic structure. This is why the chords were always in pairs. The basic pairing was often concealed with a variety of figurations, but pairs were the general method. But it didn't have to be this way. Here is the basic structure of a typical sequence:
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But you could use a sequence of three chords rather than just two:
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That is just a tiny variation, but there are probably a thousand others. What if you had different rhythmic layers for each voice, for example? As we can see from a lot of the so-called 'minimalist' composers, rhythm is probably the least-explored aspect of composition.
My point is that tonal (or some variation of tonal) harmony has enormous possibilities only a few of which were explored in the Baroque, Classical and Romantic eras. Just as the Classical composers discovered all sorts of new ways to use the harmonic techniques they inherited, so could we. I really don't think that harmony needs to be as static or impoverished as it often sounds today.
The Baroque era had certain aesthetic ideals that they used harmony to express. The Classical era had different aesthetic ideals that they altered harmony to express. So too with the Romantics.
So the problem isn't, I think, with the technique of harmony, which is just a device, after all. The problem is perhaps with our aesthetic ideals.
UPDATE: My apologies! I was in a bit of a hurry when I created my examples and in the second one above, the "Altered Sequence" I managed to write parallel octaves. That wasn't the kind of innovation I was seeking! What I should have written in the soprano voice in the final measure was C, Bb, A.