So, is this all the elements or the theory or is anything missing?

The widely held belief (as conjured upon the mistaken identity of the Celts living in the Danube basin (as per mis-reading Herodotus) and built upon with the idea of 'imperial' acculturation) is that Halstatt culture represents the 'Celtic Homeland' and that they, through expansion, have 'celticised' the majority of Europe. Cognate to this narrative is the idea that the Celtic language also begins here and is spread by that same expansion.

Problems: There is no archaeological evidence (nor does genetic evidence give any credence to) the expansion of any alleged Halstatt kingdoms into the rest of Europe; the material culture seems to be, simply that - an acceptance of material forms and techniques. Also the recent discovery of (or, more accurately, recent work on understanding the language as being) Celtic languages in South-Western Iberia pre-dating Halstatt culture.

Simply put, if Celtic cultural spread is what it is taken to be, then any evidence of migration is pretty limited. We do know of migration from this area from historical accounts and from archaeological finds, but they are not evidenced within the British isles or the Iberian peninsula. Equally the language argument seems to ignore this lack of migratory evidence, and also the limited contacts between areas.

As for the Celtic cognation....this is a self-circular argument; ie the areas defined as Celtic by the narrative are, therefore, assumed to be Celtic - thus any inscriptions are axiomatically Celtic. This has lead to, for example, the filling out of the limited Gaulish lexicon by Galatian imports. The Galatian language was assumed (on the basis of the narrative) to be the same as Gaulish.

Here's where Koch's argument becomes circumspect. He is aware of how embedded the narrative is (it is taken as the 'truth' despite it's dodgy origins). That the language(s) developed along the Atlantic seaboard must be seen as a distinct development, subject - prior to the Celtic Tartessian inscriptions - to a large degree of isolation from the central European zone, and that what contact there was for the majority of that language's evolution was limited. This comes down to the age of language groups. Neither proto-Italic or proto-Germanic languages are believed to be 6000 years old, nor should any proto-Celtic language be, for it would essentially then be PIE. So, by suggesting that proto-Celtic is a much deeper stratum he is describing something other than the usual context of proto-Celitc which, with proto-Germanic and proto-Italic, are post PIE language groups with separate paths. This deeper stratum would be pre-Germanic, pre-italic and (if it is to be viewed as a separate language path) proto-Celtic. He is, by definition, describing something other than proto-Celtic (as the term is currently understood).

What this amounts to is that the language groups of Europe are probably more finely grained than has been commonly held.