In the word blockälteste, what syllable (or syllables) gets the stress, please? Obviously not a word people say too often—and I cannot find a pronunciation for it online.
In fact, as a general rule, in compounds it is the first element (or root) that gets the primary stress. See for yourself: Autobahn, Wohnungstür, Herbstwetter, Kontrollflußgraph, etc. More notable still, this is actually quite similar to how things work in English, another Germanic language — the canonical examples in any Linguistics 101 being black board (just a noun and an adjective, equal stress on both words) vs. blackboard (compound, stress on the first element); white house vs. White House; nice rack vs. coat rack; and so on and so forth.
Back to German, though, and there to secondary stress. The longer the compound, the more likely is it to get secondary stress(es), effectively getting "broken up" into smaller compounds (compare: Kontrollflußgraph vs. Kontrollflußgraphvisualisierungssoftware vs. Kontrollflußgraphvisualisierungssoftwareentwicklerbüro ).