Both you and your friend are framing in terms of "simplicity" vs. "complexity" what's really a slightly different issue, etymological transparency vs. etymological opacity. Or, in the most basic terms, native vs. borrowed. Most people speak a language that has a layer of "erudite" vocabulary borrowed from the language of a more influential, and usually "older", culture: depending on where you are in the world, it's usually one of Latin, Chinese, or Arabic. This means there are certain lexemes, and sometimes a certain amount of grammar, that you have to learn from scratch on top of your native language if you are to understand this "erudite" layer.
For example, most speakers of English can break down the word "independence" as far as "depend", which is still a borrowed "erudite" word; speakers of Romance languages have it easier, since the Latin root
-pend- is still transparent to them as meaning "hang", in the most everyday sense, and so indépendance or indipendenza still discernibly contain the metaphor of no longer "hanging off" of something (over a presumed cliff).
So the solution — if you choose to think of this as a problem — is not in "pruning" the language, but in nativising its vocabulary. It's already been done in a lot of languages; the German Unabhängigkeit, or the Russian nezavisimost', are exact translations, or "calques", of the Latin independentia: "non-off-hang-ing-ness". That said, both Russian and German still contain a lot of Latin vocabulary, although much less that English. Very few languages have gone the way of near-complete nativisation, Icelandic being one famous example. It's hard to tell whether it did or did not lead to any greater political awareness, but it clearly involved no "pruning" of the language — if anything, it was the opposite, a massive infusion of new words.
Another point must also be raised: political vocabulary is essentially jargon, no different in principle from the jargon of seafaring or video gaming. By which I mean, it developed as a form of communication between people with specific shared experiences, trading transparency of meaning for speed, efficiency, and not the least, the ability to identify with the group. The reason we have Latinate political terms such as "consensus" was that, a long time ago, it was part of a jargon shared by people who (1) knew Latin and (2) had political phenomena as part of their everyday experience; then it was handed down generations to people who didn't necessarily know Latin anymore, but for whom a certain amount of Latin vocabulary came with the job requirements (as well as general social status). It's understandable that they weren't in any way motivated to abandon this vocabulary in favour of something more transparent to the less educated populace — unless they were of a specific type of political creed, nationalist or "national revivalist". Movements of that sort in several different countries have in fact affected many languages, and in a generally positive way at that.
But they were dedicated movements. By default, it's still up to the individual speaker whether they feel it necessary to expand their vocabulary with Latinate (or, say, Arabesque) political jargon. Not everyone has equal opportunities here, as regards time investment and the availability of knowledge (though that's less of an issue now that we have the internet). So your friend has a point. "Complex" speech isn't necessarily always inherenty valuable; often it exists just because a relatively small circle of people has found it convenient. However, you can't just decree a sweeping language reform, or manufacture the political will and popular support for it out of thin air. It's still mere reality of life that if you want to understand politicians, you might have to take time to learn new words. I'm not sure, however, that this is one of the "better" reasons, or that such better reasons even exist, beyond the most basic "knowing more is better than knowing less".