You've hit upon one of the key insights in modern linguistic theory! :D
You are partially right in your observations. Humboldt actually made the opposite observation, that an isolating language is the more 'primitive' form, and languages tend to become morphologically complex afterwards (i.e. become agglutinative), and finally the morphological boundaries become less clear (i.e. the language becomes fusional). Humboldt's process is linear, like yours.
However, it was later discovered by Gabelentz that fusional languages tend to become isolating. So he closed the loop, resulting in a cycle: Isolating -> Agglutinative -> Fusional -> Isolating...
Note that a common error is to regard this cycle as bidirectional. It is not; it is unidirectional, because when a language reaches, say, another isolating state after passing through the agglutinative and fusional states, the new language is no longer the same as the original isolating one.
Why does this happen? This question is adequately answered by the modern theory of grammaticalisation. The expression of meaning in the grammar goes through several stages. This cline is roughly as follows:
Syntactic word > Clitic > Affix > Suprasegmental > Zero
Roughly, when a lot of grammatical categories are at the two ends of this spectrum, you have an analytic language; if a lot of grammatical categories are in-between, you have a synthetic one.
When a periphrastic syntactic construction is used a lot, the words used it in will become functional, i.e. used for expressing grammatical meaning, for example while in English (still used in its original, concrete sense in phrases like 'in a while'). When these functional words become unstressed and cliticise to the words afterwards, they become clitics, such as the French article le, from the Latin demonstrative ille. Clitics can then become affixes. For example, the French adverb marker ment is a full clitic these days, but it used to be a clitic in Old French, e.g. [humble e douce]=ment. An affix can later become a suprasegmental; for example, in Old Chinese, *-s was (among other things) a causative suffix, but this later became a tone difference after tonogenesis in Middle Chinese, and some of this is retained in modern Chinese. And finally, an old distinction can simply disappear altogether; this is the cause for some of the Middle Chinese tonal differences.
So in effect, the cycle is a fall-out of these diachronic processes in which words tend to be used frequently, become entrenched, enter the grammatical system, and go through successive stages of weakening until they eventually disappear.
So how does the final isolating language become agglutinative again? Simple: New words will simply be grammaticalised into the system again. One ongoing example of this is the be going to construction in English. As will becomes more and more grammatical, be going to is replacing will's older, 'more expressive' use. The same thing is happening in French: the aller + infinitive construction is similar to be going to in this respect. These periphrastic constructions will then go through the grammaticalisation process again: the development of gonna in casual speech is the first step in this.
To conclude, yes, you're right, the transitions are unidirectional. Yet it is also cyclic, and language change doesn't 'end' at isolating.
References (for Indo-European examples):
Hopper, P. J., & Traugott, E. C. (2003). Grammaticalization. Cambridge University Press.