I don't necessarily think that all of the historical assumptions in the question are accurate.
In the old days they actually never spoke about chords. They just
wrote a bass not and added eg 64. Simple organum or basso continuo
talked about intervals.
Well, they didn't always think of "chords" in the way we think of them (i.e., as collections of pitch classes that can be inverted and are all the "same thing"). To Bach, a C-E-G "chord" was definitely not the same as a G-C-E chord with the G in the bass ("6/4"). In that, you are certainly correct. Those entities had completely different functions -- the former was a consonant triad, while the latter was a dissonant collection of notes that required resolution according to specific rules.
However, it's one thing to recognize that earlier composers put a greater emphasis on intervallic relationships between parts and on the counterpoint that results. It's much more extreme, though, to claim that they never thought about the vertical sonorities as a whole. Whether they called them "chords" or some other term, Bach knew what a 6/4 figured bass represented and how to resolve it, and he knew it was different from a 6/5 and also different from a 6/3. He also likely recognized a significantly greater kinship between a 5/3 with the same notes as a 6/3, but these were definitely different from a 6/4 with the same notes.
It wasn't just the intervals by themselves, but the vertical collections that assumed functions. And composers from their very first keyboard lessons would have spent learning patterns of vertical structures for harmonization. (See, for example, the well-known "Rule of the Octave" which taught chordal patterns for harmonizing ascending and descending scales.) When they learned counterpoint patterns, they would have known that it wasn't just two voices combined to create certain intervals, but often interactions between three or sometimes four voices that made certain kinds of textures and patterns possible. Again, whether you call these vertical sonorities "chords" with the modern meaning, historical composers definitely understood vertical collections as having particular functions and patterns before Roman numerals existed.
On the other hand, you have a good point that modern theory that tends to focus on vertical classification can miss a lot about how historical composers understood their own music. A lot of harmony did ultimately develop out of intervals and melodic interactions. Even the basic authentic cadence, which we may think of as the quintessential "harmonic" vertical gesture, was gradually built out of individual motions of melodic lines over centuries.
That is, the standard chant tenor line often descended through scale degrees 2-1. In the earliest organum, this began to be harmonized with 7-8 melodic patterns introducing a leading tone. By the 14th century, a standard other voice could be added that resolved 4-5 (or #4-5 in a "double-leading tone cadence"). In the 15th century, a fourth voice gradually was added, and eventually it migrated to the bass and became the 5-1 bass leap. In the 16th century, the 4-5 motion often became a 4-3 motion to create a complete triad at cadences, as the triad was accepted as a reasonable consonance to end on (rather than the "open fifth" sonority that was generally viewed as the best cadence in earlier times).
Thus, all of the voices of the standard V-I cadence developed out of intervallic relationships and melodic interactions. However, once that motion became a standard pattern, composers began to use those vertical collections of notes to create something akin to modern "functional harmony." One begins to see "circle of fifths" motion in sequences as in a iii-vi-ii-V-I progression as early as the time of Palestrina. Composers took those vertical patterns of voice motions and used them to build up the counterpoint patterns I mentioned above. Thus, by the time of Bach, there was a whole repertory of these sorts of patterns that composers would have learned, and a large part of some of those patterns were the vertical sonorities as well as the contrapuntal motion.
In sum, historical composers likely understood harmony a lot differently than we do today. However, back to the earliest forms of polyphony, composers also understood that certain kinds of vertical patterns of "chords" could be reused in different circumstances. It would be more accurate to say that historical composers based their "harmony" both on vertical structures and on horizontal motion, and the horizontal element was likely of much greater importance to them than it is often taught today. That only really began to change significantly in the 19th century.
For a final example, I recall a fascinating article a few years ago on cadences in Mozart that showed that Mozart clearly still was thinking of cadences as collections of individual voices resolving in particular ways, rather than as purely vertical structures. This is apparent because of the way Mozart treats cadences with the old characteristic suspension dissonance differently from cadences without the suspension. The suspension is the 8-7-8 motion found in a strong-weak-strong pattern that is a common to such diverse cadences as I64-V-I, ii65-V-I, V65/V-V-I, and a V with a 4-3 suspension resolving to I. All of these have the characteristic dissonant suspended tonic note resolving down to leading tone that dates back to the 14th century. Mozart treated those cadences differently -- and as stronger -- than, say, a IV-V-I cadence that lacks the traditional suspension. Such a distinction appears to fall away gradually for many composers in the 19th century.
So, by ignoring this historical emphasis on intervallic and contrapuntal relationships, we're likely missing out on a lot of details about how 18th century composers (and earlier) understood their music. On the other hand, it's inaccurate to say that Mozart simply "wrote a bass note and added a few intervals on top." Mozart understood that vertical sonorities ("chords") created patterns that could be reused. And it was those patterns that theorists like Rameau and his followers built theories of functional harmony on, which ultimately led to things like our modern Roman numeral method of analysis and understanding.
