This is a) not true, b) the transition to writing has a large effect on the language, not the contact with the western world, and c) I suspect you meant "analytic"/"syntactic" rather than "simple"/"complex". Neither is strictly more complex than the other, although syntactic languages typically require memorizing more forms.
A few notes. First, analytic languages seem simpler but require just as much understanding of how the words interact; this learning is not typically reflected in terms of memorization. Second, there is no obvious complexity gradient at ALL—even in languages that appear to drop "features", it's typically because of absorption and/or emergence of other features. For example, look at english—some parts are very "simple", but the language as a whole is about as complex as it gets and is NOT easy to learn. In contrast, a highly syntactic language (e.g. most early PIE languages—polyphonic greek, sanskrit, classical latin) seems more complex because so much memorization is necessary to use features together, but the lack of irregularities through loan words compensate.
In addition, it's far easier to learn complex forms by listening rather than writing. IMHO syntactic languages get a bad rep because of this.
So firstly. Syntactically speaking, languages generally have become more complex over time.
When it comes to sound change (phonology) though, things are getting simpler. This is due to external (language interaction) and internal change. Internally, we tend to ease articulation over time, we tend to evolve words to increase perceptual clarity and we tend to introduce sound systems with symmetry. By symmetry I mean, for example, sounds which activate your larynx (AKA "voiced" as in "b" in "boy") naturally create room for an unvoiced pairing like "p" in "pair". Or a vowel sound from the lower back of your mouth like "a" in "father" will incentivize a lower front sound like "a" in "sat". A high back sound like "oo" in "pool" will lead the way for use of a high front sound like "ea" in "seat".
Lots of internal as well as external processes at play which tend to evolve things towards a more efficient and simple phonological system.
On a more complicated level we have the interaction between morphological (word formation) and syntactic (word arrangement) components. According to my notes the motivating force behind morphological change (and to a lesser extent, syntactic change) is analogy. Not analogy as in the common definition; but analogy as in the process in which one form becomes like another form with which it's associated. For example, "kine" has been replaced by "cows" so that it better conforms to expected pluralization practices. Think of the mistakes children make saying things like "foots" and consider this an untainted window into our brain's natural grammar system. Analogy here serves to remove irregularities and this might be what has you thinking things are getting less complex.
You also might be interested in the evolution of English from a more inflection based language to a more analytic one. Inflection languages create grammatical distinctions with morphological affixes. Like prefixes or suffixes, they are attached to words for things like tense. An analytic language like Modern English has lost a lot of it's inflection and uses word order and function words (prepositions, articles, conjunctions) to indicate grammatical relationships.
I've got a 70% right now and the guy beside me has a 95%... so that's the best I can do in this moment. Thanks for forcing my procrastination into productivity.
In this case, it's not that languages naturally simplified, but that there were external forces driving it.
And it helps to remember that reconstructed languages only take us back so far (where they can be reconstructed at all); there's no reason not to believe that language (as opposed to "mere" communication) has been around at least as long as the species has been, so it's had a lot of time to fester, grammaticalize common concepts, overgrow, rot, have chance encounters with other, equally-esoteric languages at levels below those that would force simplification, etc. (We only have to go back to the 15th century to find William Caxton complaining that "English" was really a set of almost mutually-incomprehensible languages, and realising that he would be guiding the language in one way or another by the words he chose when making his translations.)
Language may have started out simple, but it rarely stays that way unless it needs to be shared with "outsiders". Cree, Tsez or Nama/Khoekhoe would melt the average adult American's or European's brain, but their native speakers can handle them while tired, ill and intoxicated. If by some fluke of history any of them were to become a dominant language learned by outsiders (after childhood), they'd become a whole lot less, um, interesting.
Computer languages are constructed by a single party, with a logic and purpose behind every feature, and the flexibility to make unilateral decisions about their design. It’s reasonable that they should start simply and grow in complexity.
Spoken languages, by contrast, evolve out of a behavior soup. There are no rules, particularly in the early days—just look at how long English spelling went without standardization. In an environment without rules, an unnecessarily large number of solutions to a small set of problems will develop; everyone is re-inventing the wheel. As culture solidifies, rules emerge. Best practices and linguistic “cow paths” are formed, and something resembling design emerges from the muck.
http://en.wikipedia.org/wiki/Creole_language
They end up with features that are separate from the parent languages.
I guess it is not without controversy, but there is a somewhat famous case of children inventing a language (re what you are getting at, the later children added things like verb agreement):
German has four cases, Polish seven(?), Russian six(?). In English it's mostly gone, but we occasionally have to go to the effort of distinguishing between subject and object (I/me, he/him, she/her).
For example I can't think of a programming language that is being praised for mere added complexity. Rather the opposite.