Switzerland's isn't so young either. It dates back to Napoleonic times.

Places like the US and UK need to change their system, but politicians have an incentive not to change anything.

Fortunately with the US, its decentralized system allows experimentation at the state and local level. My city (Portland, OR) just switched to ranked choice voting for city council along with a host of other changes. Voters statewide will soon be able to vote on using RCV for state races. Meanwhile, ranked choice has been implemented in several other states and localities across the country. It will take a while, but I think ranked choice will become the norm within a few decades.

Would France classify as an older system since they have a non-proportional 2-round system?

relatively homogenous

Some may be surprised by the cultural diversity this rather small country packs:

It has four main linguistic and cultural regions: German, French, Italian and Romansh. Although most Swiss are German-speaking, national identity is fairly cohesive, being rooted in a common historical background, shared values such as federalism and direct democracy,[15][page needed] and Alpine symbolism.[16][17] Swiss identity transcends language, ethnicity, and religion, leading to Switzerland being described as a Willensnation ("nation of volition") rather than a nation state.[18]

Due to its linguistic diversity, Switzerland is known by multiple native names: Schweiz [ˈʃvaɪts] (German);[f][g] Suisse [sɥis(ə)] (French); Svizzera [ˈzvittsera] (Italian); and Svizra [ˈʒviːtsrɐ, ˈʒviːtsʁɐ] (Romansh).[h] On coins and stamps, the Latin name, Confoederatio Helvetica — frequently shortened to "Helvetia" — is used instead of the spoken languages.

I also think the local traditions differentiating down to single villages are more important and alive than in other countries.

But yes, "national identity is fairly cohesive", maybe you meant that.